Expressions & Equations - 7th Grade Math

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Question

Sarah is going to buy a new cell phone. The cell phone costs $\$175$ plus a sales tax. What is the total price that Sarah will pay for her new cell phone?

Answer

We know that Sarah is going to pay of the $\$175$ cell phone because that is the total cost. Plus, she is going to pay of the $\$175$ because that is the sales tax.

First, we need to convert our percentages into decimals in order to multiply.

$100%\rightarrow1.00$

$10%\rightarrow0.10$

Next, we can write a numeric expression and solve:

$1.00($175)+0.10($175)=1.10(\$175)$

$\$175+$17.50=$192.50$

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Question

Megan is going to buy a new TV. The TV costs $\$375$ plus a sales tax. What is the total price that Megan will pay for her new TV?

Answer

We know that Megan is going to pay of the $\$375$ TV because that is the total cost. Plus, she is going to pay of the $\$375$ because that is the sales tax.

First, we need to convert our percentages into decimals in order to multiply.

$100%\rightarrow1.00$

$10%\rightarrow0.10$

Next, we can write a numeric expression and solve:

$1.00($375)+0.10($375)=1.10(\$375)$

$\$375+$37.50=$412.50$

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Question

Olivia is going to buy a new computer. The computer costs $\$250$ plus a sales tax. What is the total price that Olivia will pay for her new computer?

Answer

We know that Olivia is going to pay of the $\$250$ computer because that is the total cost. Plus, she is going to pay of the $\$250$ because that is the sales tax.

First, we need to convert our percentages into decimals in order to multiply.

$100%\rightarrow1.00$

$10%\rightarrow0.10$

Next, we can write a numeric expression and solve:

$1.00($250)+0.10($25)=1.10(\$250)$

$\$250+$25=$275$

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Question

Meredith is going to buy a new coat. The coat costs $\$100$ plus a sales tax. What is the total price that Meredith will pay for her new coat?

Answer

We know that Meredith is going to pay of the $\$100$ coat because that is the total cost. Plus, she is going to pay of the $\$100$ because that is the sales tax.

First, we need to convert our percentages into decimals in order to multiply.

$100%\rightarrow1.00$

$10%\rightarrow0.10$

Next, we can write a numeric expression and solve:

$1.00($100)+0.10($100)=1.10(\$100)$

$\$100+$10=$110$

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Question

Gail is going to buy a new camera. The camera costs $\$150$ plus a sales tax. What is the total price that Gail will pay for her new camera?

Answer

We know that Gail is going to pay of the $\$150$ cell phone because that is the total cost. Plus, she is going to pay of the $\$150$ because that is the sales tax.

First, we need to convert our percentages into decimals in order to multiply.

$100%\rightarrow1.00$

$10%\rightarrow0.10$

Next, we can write a numeric expression and solve:

$1.00($150)+0.10($150)=1.10(\$150)$

$\$150+$15=$165$

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Question

Elizabeth is going to buy concert tickets. The concert tickets costs $\$200$ plus a sales tax. What is the total price that Elizabeth will pay for her concert tickets?

Answer

We know that Elizabeth is going to pay of the $\$200$ concert because that is the total cost. Plus, she is going to pay of the $\$200$ because that is the sales tax.

First, we need to convert our percentages into decimals in order to multiply.

$100%\rightarrow1.00$

$10%\rightarrow0.10$

Next, we can write a numeric expression and solve:

$1.00($200)+0.10($200)=1.10(\$200)$

$\$200+$20=$220$

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Question

Tamara is going to buy a new cell phone. The cell phone costs $\$170$ plus an sales tax. What is the total price that Tamara will pay for her new cell phone?

Answer

We know that Tamara is going to pay of the $\$170$ cell phone because that is the total cost. Plus, she is going to pay of the $\$170$ because that is the sales tax.

First, we need to convert our percentages into decimals in order to multiply.

$100%\rightarrow1.00$

$8%\rightarrow0.08$

Next, we can write a numeric expression and solve:

$1.00($170)+0.08($170)=1.08(\$170)$

$\$170+$13.60=$183.60$

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Question

Laura is going to buy a new TV. The TV costs $\$400$ plus a sales tax. What is the total price that Laura will pay for her new TV?

Answer

We know that Laura is going to pay of the $\$400$ TV because that is the total cost. Plus, she is going to pay of the $\$400$ because that is the sales tax.

First, we need to convert our percentages into decimals in order to multiply.

$100%\rightarrow1.00$

$8%\rightarrow0.08$

Next, we can write a numeric expression and solve:

$1.00($400)+0.08($400)=1.08(\$400)$

$\$400+$32=$432$

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Question

Addison is going to buy a new computer. The computer costs $\$575$ plus an sales tax. What is the total price that Addison will pay for her new computer?

Answer

We know that Addison is going to pay of the $\$575$ computer because that is the total cost. Plus, she is going to pay of the $\$575$ because that is the sales tax.

First, we need to convert our percentages into decimals in order to multiply.

$100%\rightarrow1.00$

$8%\rightarrow0.08$

Next, we can write a numeric expression and solve:

$1.00($575)+0.08($575)=1.08(\$575)$

$\$575+$46=$621$

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Question

Liz is going to buy a new coat. The coat costs $\$55$ plus an sales tax. What is the total price that Liz will pay for her new coat?

Answer

We know that Liz is going to pay of the $\$55$ coat because that is the total cost. Plus, she is going to pay of the $\$55$ because that is the sales tax.

First, we need to convert our percentages into decimals in order to multiply.

$100%\rightarrow1.00$

$8%\rightarrow0.08$

Next, we can write a numeric expression and solve:

$1.00($55)+0.08($55)=1.08(\$55)$

$\$55+$4.40=$59.40$

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Question

Christina is going to buy a new camera. The camera costs $\$220$ plus an sales tax. What is the total price that Christina will pay for her new camera?

Answer

We know that Christina is going to pay of the $\$220$ camera because that is the total cost. Plus, she is going to pay of the $\$220$ because that is the sales tax.

First, we need to convert our percentages into decimals in order to multiply.

$100%\rightarrow1.00$

$8%\rightarrow0.08$

Next, we can write a numeric expression and solve:

$1.00($220)+0.08($220)=1.08(\$220)$

$\$220+$17.60=$237.60$

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Question

Kara is going to buy concert tickets. The tickets cost $\$325$ plus a sales tax. What is the total price that Kara will pay for her concert tickets?

Answer

We know that Kara is going to pay of the $\$325$ concert tickets because that is the total cost. Plus, she is going to pay of the $\$325$ because that is the sales tax.

First, we need to convert our percentages into decimals in order to multiply.

$100%\rightarrow1.00$

$8%\rightarrow0.08$

Next, we can write a numeric expression and solve:

$1.00($325)+0.08($325)=1.08(\$325)$

$\$325+$26=$351$

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Question

Define an operation $\bigstar$ on the set of real numbers as follows:

$a \bigstar b = \frac{a+b}{ab}$ .

$a \bigstar (-1) = 1$ . What is the value of ?

Answer

$a \bigstar b = \frac{a+b}{ab}$

and

$a \bigstar (-1) = 1$

so

$\frac{a+(-1)}{a(-1)}=1$

$\frac{a-1}{-a} = 1$

$\frac{a-1}{-a} \cdot (-a) = 1 \cdot (-a)$

$2a \div 2 = 1 \div 2$

$a = \frac{1}{2}$

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Question

Define an operation $\bigstar$ on the set of real numbers as follows:

$a \bigstar b = a^{2}+ b$

If $6 \bigstar b = 100$ , then what is ?

Answer

$a \bigstar b = a^{2}+ b$ ,

so

$6 \bigstar b = 6 ^{2} + b = 36 + b$ .

If

$6 \bigstar b = 100$

then

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Question

Define an operation $\bigstar$ on the set of real numbers as follows:

$a \bigstar b = \frac{a+b}{ab}$ .

If $a \bigstar \frac{1}{2} = -1$ , evaluate .

Answer

$a \bigstar b = \frac{a+b}{ab}$

so

$a \bigstar \frac{1}{2} = \frac{a+ \frac{1}{2} }{a \cdot \frac{1}{2} } = \frac{\frac{2a}{2}+ \frac{1}{2} }{ \frac{a}{2} } = \frac{\frac{2a+1}{2} }{ \frac{a}{2} }$

Equivalently

$a \bigstar \frac{1}{2} = \frac{2a+1}{2} \div \frac{a}{2} = \frac{2a+1}{2} \cdot \frac{2}{a} = \frac{2a+1}{a}$

$a \bigstar \frac{1}{2} = -1$ , so set this equal to :

$\frac{2a+1}{a} = -1$

$\frac{2a+1}{a} \cdot a = -1 \cdot a$

$3a\div 3 = - 1 \div 3$

$a = - \frac{1}{3}$

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Question

Define an operation $\bigstar$ on the set of real numbers as follows:

$a \bigstar b = \frac{a+b}{ab}$ .

If $a \bigstar 0.5 = 0.1$ , then evaluate .

Answer

$a \bigstar b = \frac{a+b}{ab}$ ,

so

$a \bigstar 0.5 = \frac{a+0.5 }{a \cdot 0.5 } = \frac{a+0.5 }{0.5a }$

Set this equal to 0.1:

$\frac{a+0.5 }{0.5a } = 0.1$

$\frac{a+0.5 }{0.5a } \cdot 0.5 a = 0.1 \cdot 0.5 a$

$(a+0.5) \cdot 100 = 0.05 a \cdot 100$

$a \cdot 100 +0.5 \cdot 100 = 5 a$

$50 \div (-95) = -95a \div (-95)$

$a = -\frac{50}{95} = - \frac{10}{19}$

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Question

Define an operation $\bigstar$ on the set of real numbers as follows:

$a \bigstar b = \frac{ab}{a+b}$

$a \bigstar 1= -1$ . What is the value of ?

Answer

$a \bigstar b = \frac{ab}{a+b}$ , so

$a \bigstar 1 = \frac{a \cdot 1 }{a+1} = \frac{a }{a+1}$

Set this equal to :

$\frac{a }{a+1} = -1$

$\frac{a }{a+1} \cdot (a+1) = -1 \cdot (a+1)$

$2a \div 2= - 1 \div 2$

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Question

If a server at a restaurant gets a tip on a bill of $\$25$ , then what will be the amount of the tip?

Answer

The first step to solving this problem is determining what operation we are going to use.

We know that the tip is going to be of $\$25$ . The keyword "of" gives us a clue and indicates that we are going to multiply.

As we have learned in previous lessons, we need to convert our percentage into a decimal before we are able to multiply:

$20%\rightarrow0.20$

Next, we can perform the multiplication operation and find the tip:

$\frac{\begin{array}[b]{r}25\ \times\ .20\end{array}}{ \ \ \space 5.00}$

The server's tip will be $\$5.00$

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Question

If a server at a restaurant gets a tip on a bill of $\$29$ , then what will be the amount of the tip?

Answer

The first step to solving this problem is determining what operation we are going to use.

Think:we know that the tip is going to be of $\$29$ . The keyword "of" gives us a clue and indicates that we are going to multiply.

As we have learned in previous lessons, we need to convert our percentage into a decimal before we are able to multiply:

$20%\rightarrow0.20$

Next, we can perform the multiplication operation and find the tip:

$\frac{\begin{array}[b]{r}29\ \times\ .20\end{array}}{ \ \ \space 5.80}$

The server's tip will be $\$5.80$

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Question

If a server at a restaurant gets a tip on a bill of $\$17$ , then what will be the amount of the tip?

Answer

The first step to solving this problem is determining what operation we are going to use.

Think:we know that the tip is going to be of $\$17$ . The keyword "of" gives us a clue and indicates that we are going to multiply.

As we have learned in previous lessons, we need to convert our percentage into a decimal before we are able to multiply:

$20%\rightarrow0.20$

Next, we can perform the multiplication operation and find the tip:

$\frac{\begin{array}[b]{r}17\ \times\ .20\end{array}}{ \ \ \space 3.40}$

The server's tip will be $\$3.40$

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