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

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Question

After a discount, a car costs $\$6,000$ . How much did the car cost before the discount?

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Answer

Let be the cost of the car before the discount. Since we know that the car at a discount costs $\$6,000$ , we can write the following equation:

Now, solve for to find the cost of the car before the discount.

$x=\frac{6000}{0.75}$

The car originally cost $\$8,000$ before the discount was applied.

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Question

There are yellow marbles in a bag. If of the marbles in the bag are yellow, how many total marbles are in the bag?

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Answer

Let be the total number of marbles in the bag. Since we know that of the marbles are yellow, we can set up the following equation and solve for :

$x=\frac{10}{0.125}$$

There are total marbles in the bag.

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Question

Byron eats calories for lunch. If he eats of his calories at lunch, what is the total number of calories he eats for the day?

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Answer

Let be the total number of calories Byron eats in a day. With the information given in the question, we can write the following equation and solve for .

$x=\frac{600}{0.25}$$

Byron eats calories for the day described in the question.

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Question

Max bought a t-shirt that was on sale at the store for . If he paid $\$15.00$ for the shirt, how much would the shirt have costed before the sale?

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Answer

Let be the cost of the t-shirt before it went on sale. With the information given in the question, we can write the following equation and solve for .

This can be rewritten as:

$x=\frac{15}{0.85}$

The shirt cost $\$17.65$ before the sale.

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Question

Roselyn spent $\$20.25$ when she bought a vacuum that was off. How much did the vacuum cost before the sale?

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Answer

Let be the cost of the vacuum before the sale. With the information given in the question, we can write the following equation and solve for .

This can be rewritten as:

$x=\frac{20.25}{0.82}$

The vacuum cost $\$24.70$ before it went on sale.

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Question

When Teresa saw that plane tickets to Hong Kong were off, she immediately bought a discounted ticket for $\$850$ . How much would the ticket have cost if tickets to Hong Kong were not on sale?

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Answer

Let be the price of the non-discounted ticket. With the information given in the question, we can write the following equation and solve for .

$x=\frac{850}{0.65}$

The plane ticket that Teresa bought would have cost $\$1307.69$ if it were not on sale.

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Question

There are red marbles in a bag. If of the marbles in the bag are red marbles, how many total marbles are in the bag?

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Answer

Let be the total number of marbles in the bag. With the information given in the question, we can write the following equation and solve for .

$x=\frac{12}{0.75}$$

There are total marbles in the bag.

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Question

If of a certain number is , what is that number?

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Answer

Let be the number we are looking for. With the information given in the question, we can write the following equation and solve for .

$x=\frac{112}{0.125}$$

of is , so is the correct answer.

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Question

If $\frac{1}{5}$ of a certain number is , what is that number?

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Answer

Let be the number we are looking for. With the information given in the question, we can write the following equation and solve for .

$$\frac{1}{5}$x=50$

$\frac{5}{1}$($\frac{1}{5}$x)=(50)$\frac{5}{1}$

$\frac{1}{5}$ of is , so is the correct answer.

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Question

If $\frac{3}{7}$ of a certain number is , what is that number?

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Answer

Let be the number we are looking for. With the information given in the question, we can write the following equation and solve for .

$$\frac{3}{7}$x=60$

$\frac{7}{3}$($\frac{3}{7}$x)=(60)$\frac{7}{3}$

$x=\frac{60\cdot 7}{3}$$

$x=\frac{420}{3}$$

$\frac{3}{7}$ of is , so is the correct answer.

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Question

Last year, of students at a certain high school continued on to college. If students from this high school went to college, how many total students did the high school have last year?

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Answer

Let be the total number of students enrolled last year at the high school the question describes. With the information given in the question, we can write the following equation and solve for .

$x=\frac{1400}{0.7}$$

of is , so the high school the question describes had students last year.

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Question

students in a class are vegetarian. If of this class is vegetarian, how many total students are in the class?

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Answer

Let be the total number of students in the class. With the information given in the question, we can write the following equation and solve for .

$x=\frac{24}{0.12}$$

of is , so there are students in the class the question describes.

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Question

After a discount, a car costs $\$6,000$ . How much did the car cost before the discount?

Tap to reveal answer

Answer

Let be the cost of the car before the discount. Since we know that the car at a discount costs $\$6,000$ , we can write the following equation:

Now, solve for to find the cost of the car before the discount.

$x=\frac{6000}{0.75}$

The car originally cost $\$8,000$ before the discount was applied.

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Question

There are yellow marbles in a bag. If of the marbles in the bag are yellow, how many total marbles are in the bag?

Tap to reveal answer

Answer

Let be the total number of marbles in the bag. Since we know that of the marbles are yellow, we can set up the following equation and solve for :

$x=\frac{10}{0.125}$$

There are total marbles in the bag.

← Didn't Know|Knew It →

Question

Byron eats calories for lunch. If he eats of his calories at lunch, what is the total number of calories he eats for the day?

Tap to reveal answer

Answer

Let be the total number of calories Byron eats in a day. With the information given in the question, we can write the following equation and solve for .

$x=\frac{600}{0.25}$$

Byron eats calories for the day described in the question.

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Question

Max bought a t-shirt that was on sale at the store for . If he paid $\$15.00$ for the shirt, how much would the shirt have costed before the sale?

Tap to reveal answer

Answer

Let be the cost of the t-shirt before it went on sale. With the information given in the question, we can write the following equation and solve for .

This can be rewritten as:

$x=\frac{15}{0.85}$

The shirt cost $\$17.65$ before the sale.

← Didn't Know|Knew It →

Question

Roselyn spent $\$20.25$ when she bought a vacuum that was off. How much did the vacuum cost before the sale?

Tap to reveal answer

Answer

Let be the cost of the vacuum before the sale. With the information given in the question, we can write the following equation and solve for .

This can be rewritten as:

$x=\frac{20.25}{0.82}$

The vacuum cost $\$24.70$ before it went on sale.

← Didn't Know|Knew It →

Question

When Teresa saw that plane tickets to Hong Kong were off, she immediately bought a discounted ticket for $\$850$ . How much would the ticket have cost if tickets to Hong Kong were not on sale?

Tap to reveal answer

Answer

Let be the price of the non-discounted ticket. With the information given in the question, we can write the following equation and solve for .

$x=\frac{850}{0.65}$

The plane ticket that Teresa bought would have cost $\$1307.69$ if it were not on sale.

← Didn't Know|Knew It →

Question

There are red marbles in a bag. If of the marbles in the bag are red marbles, how many total marbles are in the bag?

Tap to reveal answer

Answer

Let be the total number of marbles in the bag. With the information given in the question, we can write the following equation and solve for .

$x=\frac{12}{0.75}$$

There are total marbles in the bag.

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Question

If of a certain number is , what is that number?

Tap to reveal answer

Answer

Let be the number we are looking for. With the information given in the question, we can write the following equation and solve for .

$x=\frac{112}{0.125}$$

of is , so is the correct answer.

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