How to find the part from the whole - SSAT Upper Level Quantitative

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Question

Susie won $\$10,000$ from the lottery. If she has to pay of the winnings to taxes and gives her parents of the remaining amount, how much does she have left over?

Answer

First, find out how much she has left after she pays her taxes.

$\text{After tax amount}=$10,000-($10,000\times0.45)=\$5,500$

Now, take away of the after-tax amount to find out how much she has left.

$\$5500-(0.2\times$5500)=$4,400$

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Question

Initially, number of students were going to chip in to buy their teacher a present that cost dollars. If students decide not to pay, which of the following expressions represent how much each remaining student must now pay?

Answer

To determine how much each person must pay, we will need to divide the total dollar amount by the number of people paying.

Before some students decided not to pay, the amount each person would have to pay is represented by the following expression:

$\frac{d}{m}$

Now, since students dropped out, we need to subtract that from the number of people who will be paying.

$\text{Cost per student}=\frac{d}{m-y}$

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Question

Kerry spends of his monthly salary on rent, on food, and on movies. If he spent $\$900$ on rent, how much did he spend on food?

Answer

First, find out how much Kerry makes per month. Let be his monthly salary. We know that he spends of his monthly salary on rent, and that he spends $\$900$ on rent. Knowing this, we can set up an equation and solve for , how much Kerry makes per month.

$0.45x=\$900$

$x=\frac{\$900}{0.45}$

$x=\$2,000$

Now, we can find out how much he spends on food.

$\text{Amount spent on food}=$2,000\times0.2=$400$

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Question

Pauline has pieces of candy. If she eats of the candy then accidentally drops $\frac{1}{3}$ of the remaining amount on the ground, how many pieces of candy does she have left?

Answer

First, find out how many pieces of candy Pauline has after eating of them.

$20-(0.25\times20)=15$

Now, she loses $\frac{1}{3}$ of this remaining amount. Since $\frac{1}{3}$ of is , that means that her new total is 15 - 5 = 10 pieces of candy.

Pauline is left with 10 pieces of candy.

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Question

A class of students was polled. If $\frac{1}{6}$ of them claimed that they enjoy eating sushi, how many students enjoy eating sushi?

Answer

Multiply the total number of students by the fraction to find out how many of them enjoy eating sushi.

$30\times\frac{1}{6}=\frac{30}{6}=5$

students in the class enjoy eating sushi.

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Question

A car is on sale for off. If the original price is $\$9,000$ , how much does the car cost when it is on sale?

Answer

Subtract the discount from the original price of the car.

$$9000-(0.375\times$9000)=\$5625$

The discounted car costs $\$5,625$ .

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Question

Jeremy bought $\$10.21$ worth of toothpaste. At the checkout, he found that he had a coupon that would take off the cost of the toothpaste. How much will Jeremy pay for the toothpaste if he uses the coupon?

Answer

Subtract the amount the coupon would take off from the total amount the toothpaste would cost.

$$10.21-(0.2\times$10.21)=\$8.17$

If Jeremy uses the coupon, the toothpaste will cost $\$8.17$ .

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Question

What is of ?

Answer

Multiply by to find the answer.

$250\times0.54=135$ .

$135 \text{ is }54%\text{ of }250.$

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Question

The tax on the sale of a house worth $\$150,560$ was $\$22,584$ . What was the tax rate?

Answer

To find the tax rate, divide the tax amount by the total worth of the house.

$22584\div150560=0.15$

Now, convert this decimal into a percentage.

$0.15\cdot\frac{100}{100}=\frac{15}{100}=15%$

The tax rate on this house sale is .

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Question

If Hannah needs to pay a tax on her yearly income of $\$36,000$ , how much does she need to pay for the tax?

Answer

Multiply $\$36,000$ by to find the amount Hannah needs to pay in taxes.

$\$36,000\times0.12=\$4,320$

Hannah needs to pay $\$4,320$ in taxes.

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Question

A dress goes on sale for off. If the dress originally cost $\$34$ , how much does it cost while it is on sale?

Answer

Subtract the amount discounted from the original cost of the dress to find its sale price.

$34-(0.32\times34)=23.12$

The dress cost $\$23.12$ on sale.

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Question

Susie won $\$10,000$ from the lottery. If she has to pay of the winnings to taxes and gives her parents of the remaining amount, how much does she have left over?

Answer

First, find out how much she has left after she pays her taxes.

$\text{After tax amount}=$10,000-($10,000\times0.45)=\$5,500$

Now, take away of the after-tax amount to find out how much she has left.

$\$5500-(0.2\times$5500)=$4,400$

Compare your answer with the correct one above

Question

Initially, number of students were going to chip in to buy their teacher a present that cost dollars. If students decide not to pay, which of the following expressions represent how much each remaining student must now pay?

Answer

To determine how much each person must pay, we will need to divide the total dollar amount by the number of people paying.

Before some students decided not to pay, the amount each person would have to pay is represented by the following expression:

$\frac{d}{m}$

Now, since students dropped out, we need to subtract that from the number of people who will be paying.

$\text{Cost per student}=\frac{d}{m-y}$

Compare your answer with the correct one above

Question

Kerry spends of his monthly salary on rent, on food, and on movies. If he spent $\$900$ on rent, how much did he spend on food?

Answer

First, find out how much Kerry makes per month. Let be his monthly salary. We know that he spends of his monthly salary on rent, and that he spends $\$900$ on rent. Knowing this, we can set up an equation and solve for , how much Kerry makes per month.

$0.45x=\$900$

$x=\frac{\$900}{0.45}$

$x=\$2,000$

Now, we can find out how much he spends on food.

$\text{Amount spent on food}=$2,000\times0.2=$400$

Compare your answer with the correct one above

Question

Pauline has pieces of candy. If she eats of the candy then accidentally drops $\frac{1}{3}$ of the remaining amount on the ground, how many pieces of candy does she have left?

Answer

First, find out how many pieces of candy Pauline has after eating of them.

$20-(0.25\times20)=15$

Now, she loses $\frac{1}{3}$ of this remaining amount. Since $\frac{1}{3}$ of is , that means that her new total is 15 - 5 = 10 pieces of candy.

Pauline is left with 10 pieces of candy.

Compare your answer with the correct one above

Question

A class of students was polled. If $\frac{1}{6}$ of them claimed that they enjoy eating sushi, how many students enjoy eating sushi?

Answer

Multiply the total number of students by the fraction to find out how many of them enjoy eating sushi.

$30\times\frac{1}{6}=\frac{30}{6}=5$

students in the class enjoy eating sushi.

Compare your answer with the correct one above

Question

A car is on sale for off. If the original price is $\$9,000$ , how much does the car cost when it is on sale?

Answer

Subtract the discount from the original price of the car.

$$9000-(0.375\times$9000)=\$5625$

The discounted car costs $\$5,625$ .

Compare your answer with the correct one above

Question

Jeremy bought $\$10.21$ worth of toothpaste. At the checkout, he found that he had a coupon that would take off the cost of the toothpaste. How much will Jeremy pay for the toothpaste if he uses the coupon?

Answer

Subtract the amount the coupon would take off from the total amount the toothpaste would cost.

$$10.21-(0.2\times$10.21)=\$8.17$

If Jeremy uses the coupon, the toothpaste will cost $\$8.17$ .

Compare your answer with the correct one above

Question

What is of ?

Answer

Multiply by to find the answer.

$250\times0.54=135$ .

$135 \text{ is }54%\text{ of }250.$

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Question

The tax on the sale of a house worth $\$150,560$ was $\$22,584$ . What was the tax rate?

Answer

To find the tax rate, divide the tax amount by the total worth of the house.

$22584\div150560=0.15$

Now, convert this decimal into a percentage.

$0.15\cdot\frac{100}{100}=\frac{15}{100}=15%$

The tax rate on this house sale is .

Compare your answer with the correct one above

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