If Bob fills a bucket with 9 logs that weigh 1.22 pounds each and the total weight of the bucket and logs 13.3 pounds, what percentage of the total weight is the bucket?

17.44%

.1744%

2.32%

18.60%

15.9%

Explanation

This question involves muliple steps to attain the correct answer.

To solve for the weight of the bucket (we will let 'x' represent this) the following equation can be set up:

To isolate x, subtract 9 * 1.22 (which is equal to 10.98) from both sides. We find x to be equal to 2.32.

The question asks us for the percentage of the total weight, so to find this, we must divide 2.32 by the total weight and multiple our answer by 100.

$\frac{2.32}{13.3}*100 = 17.44$

Rounded to two decimal points of accuracy, the final answer is 17.44%.

Which of the following phrases can be represented by the algebraic expression

$20 - \sqrt{x}$

Twenty decreased by the square root of a number

Twenty less than the square root of a number

The square root of the difference of a number and twenty

The square root of the difference of twenty and a number

Negative twenty multiplied by the square root of a number

Explanation

$20 - \sqrt{x}$ is twenty decreased by $\sqrt{x}$ , which is the square root of a number, so $20 - \sqrt{x}$ is "twenty decreased by the square root of a number".

If Jane buys four cans of soda at $1.56 each and pays $6.93 total, what is the percentage of the sales tax?

Explanation

How to calculate the amount of sales tax?

Convert tax percentage into a decimal by moving the decimal point two spaces to the left.
Multiple the pre-tax value by the newly calculated decimal value in order to find the cost of the sales tax.
Add the sales tax value to the pre-tax value to calculate the total cost.

Calculating sales tax at time of purchase:

In order to calculate the sales tax of an item, we need to first multiply the pre-tax cost of the item by the sales tax percentage after it has been converted into a decimal. Once the sales tax has been calculated it needs to be added to the pre-tax value in order to find the total cost of the item. Let's start by working with an example. If a magazine costs $2.35 and has a 6% sales tax, then what is the total cost of the item. First, we need to convert the sales tax percentage into a decimal by moving the point two spaces to the left.

$6% \rightarrow 0.06$

Now, we need to multiply the pre-tax cost of this item by this value in order to calculate the sales tax cost.

$\textup{Sales tax}=0.06\times$2.35$

$\textup{Sales tax}=$0.141$

Round to two decimal places since our total is in dollars and cents.

$\textup{Sales tax}=$0.14$

Last, add this value to the pre-tax value of the item to find the total cost.

$\textup{Total cost}=\textup{Pre-tax value}+\textup{Sales tax}$

$\textup{Total cost}=$2.35+$0.14$

$\textup{Total cost}=$2.49$

Calculating the sales tax percentage of a total:

If we are given the total cost of an item or group of items and the pre-tax cost of the good(s), then we can calculate the sales tax percentage of the total cost. First, we need to subtract the pre-tax value from the total cost of the purchase. Next, we need to create a ratio of the sales tax to the pre-tax cost off the items. Last, we need to create a proportion where the pre-tax cost is related to 100% and solve for the percentage of the sales tax. Let's start by working through an example. If a person pays $245.64 for groceries that cost $220.00 pre tax, then what is the sales tax percentage for the items.

First, subtract the pre-tax value from the total cost of the items to find the sales tax cost.

$\textup{Sales tax}=\textup{Total cost}-\textup{Pre-tax value}$

$\textup{Sales tax}=$245.64-$220.00$

$\textup{Sales tax}=$25.64$

Next, create a ratio of the sales tax to the pre-tax cost of the items.

$\frac{\textup{Sales tax}}{\ \textup{Pre-tax value}} = \frac{$25.64}{$220.00}$

Last, create a proportion where the pre-tax value is proportional to 100% and solve for the percentage of sales tax.

$\frac{$25.64}{$220.00}=\frac{\textup{Sales tax percentage}}{100%}$

Cross multiply and solve.

$$220.00\times\textup{Sales tax percentage}=$25.64\times 100%$

$$220.00\times\textup{Sales tax percentage}=$2564.00$

Isolate the sales tax percentage to the left side of the equation by dividing each side by the pre-tax value.

$\frac{$220.00\times\textup{Sales tax percentage}}{$220.00}=\frac{$2564.00}{$220.00}$

$\textup{Sales tax percentage}=11.6545455%$

Round to two decimal places since our answer is in dollars and cents.

$\textup{Sales tax percentage}=11.65%$

Last, we can check this answer by calculating the sales tax percentage of the total as seen previously.

First, we need to convert the sales tax percentage into a decimal by moving the point two spaces to the left.

$11.6545455% \rightarrow 0.116545455$

Now, we need to multiply the pre-tax cost of this item by this value in order to calculate the sales tax cost.

$\textup{Sales tax}=0.116545455\times$220.00$

$\textup{Sales tax}=$25.6400001$

Round to two decimal places since our total is in dollars and cents.

$\textup{Sales tax}=$25.64$

Last, add this value to the pre-tax value of the item to find the total cost.

$\textup{Total cost}=\textup{Pre-tax value}+\textup{Sales tax}$

$\textup{Total cost}=$220.00+$25.64$

$\textup{Total cost}=$245.64$

Our answers check out; therefore they are correct. Now, let's use this information to solve the given problem.

Solution:

If each soda cost $1.56 and Jane bought four, the total for the sodas was:

$1.56\cdot 4=6.24$

And she paid $6.93

$\frac{6.93}{6.24}=1.11$

The sales tax was 11%.

Jim sells apples for per pound and oranges for per pound. What is a formula to find the revenue for pounds of apples and pounds of oranges?

Explanation

Since you are solving for , that goes on one side of the equation. and 's revenues are based on how much they sell for per pound.

So for every pound of apples they make dollars or .

For every pound of oranges they make dollars or .

To put it all together, you get

Which of the following phrases can be represented by the algebraic expression $\frac{1}{9 - x}$ ?

The multiplicative inverse of the difference of nine and a number

The multiplicative inverse of the difference of a number and nine

Nine decreased by the multiplicative inverse of a number

Nine less than by the multiplicative inverse of a number

One divided into the difference of nine and a number

Explanation

$\frac{1}{9 - x}$ is the multiplicative inverse of , which is the difference of nine and a number. Therefore, $\frac{1}{9 - x}$ is "the multiplicative inverse of the difference of nine and a number".

Sarah sells lemonade at the concession stands. She charges fifty cents per cup of lemonade, and twenty five cents for refills. What is the equation that represents the total that she will make from the lemonade stand using the variables cups and refills ?

Explanation

Sarah charges fifty cents per cup of lemonade:

Sarah charges twenty five cents for refills:

Set up the equation by adding the totals.

The answer is:

Which of the following phrases can be written as the algebraic expression ?

Seven decreased by the opposite of a number

Seven decreased by the absolute value of a number

The opposite of the difference of seven and a number

The opposite of a number decreased by seven

The absolute value of the difference of seven and a number

Explanation

is seven decreased by , which is the opposite of a number; therefore, is "seven decreased by the opposite of a number."

Which of the following phrases can be written as the algebraic expression $\left |8-a \right |$ ?

The absolute value of the difference of eight and a number

The absolute value of the difference of a number and eight

Eight subtracted from the absolute value of a number

Eight decreased by the absolute value of a number

The absolute value of the product of negative eight and a number

Explanation

$\left |8-a \right |$ is the absolute value of , which is the difference of eight and a number. Therefore, $\left |8-a \right |$ is "the absolute value of the difference of eight and a number."

Adult tickets to the zoo sell for ; child tickets sell for . On a given day, the zoo sold $5\textup,450$ tickets and raised $$36\textup,330$ in admissions. How many adult tickets were sold?

$2\textup,270$

$2\textup,150$

$2\textup,180$

$2\textup,240$

$2\textup,310$

Explanation

Let be the number of adult tickets sold. Then the number of child tickets sold is $5\textup,450 - A$ .

The amount of money raised from adult tickets is ; the amount of money raised from child tickets is $5 \left (5\textup,450 - A \right )$ . The sum of these money amounts is , so the amount of money raised can be defined by the following equation:

$9A + 5 (5\textup,450-A) = 36\textup,330$

To find the number of adult tickets sold, solve for :

$9A + 27\textup,250-5A = 36\textup,330$

$4A + 27\textup,250 = 36\textup,330$

$4A + 27\textup,250 - 27\textup,250= 36\textup,330- 27\textup,250$

$4A = 9,080\textup$

$4A \div 4 = 9\textup,080 \div 4$

$A = 2\textup,270$

$2\textup,270$ adult tickets were sold.

Which of the following phrases can be represented by the algebraic expression

$\sqrt[3]{x} - 10$

Ten less than the cube root of a number

Ten decreased by the cube root of a number

The cube root of the difference of a number and ten

Ten less than three times the square root of a number

Ten decreased by three times the square root of a number

Explanation

$\sqrt[3]{x} - 10$ is ten less than $\sqrt[3]{x}$ , which is the cube root of a number; therefore, $\sqrt[3]{x} - 10$ is "ten less than the cube root of a number".

Equations Based on Word Problems

Help Questions

Explanation

Explanation

Explanation

How to calculate the amount of sales tax?

Calculating sales tax at time of purchase:

Calculating the sales tax percentage of a total:

Solution:

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation