Question

proportion word problems
answer each question and round your answer to the nearest whole number.

1. if you can buy one can of pineapple chunks for $2 then how many can you buy with $10?
2. one jar of crushed ginger costs $2. how many jars can you buy for $4?
3. one cantaloupe costs $2. how many cantaloupes can you buy for $6?
4. one package of blueberries costs $3. how many packages of blueberries can you buy for $9?
5. shawna reduced the size of a rectangle to a height of 2 in. what is the new width if it was originally 24 in wide and 12 in tall?
6. ming was planning a trip to western samoa. before going, she did some research and learned that the exchange rate is 6 tala for $2. how many tala would she get if she exchanged $6?
7. jasmine bought 32 kiwi fruit for $16. how many kiwi can lisa buy if she has $4?
8. if you can buy four bulbs of elephant garlic for $8 then how many can you buy with $32?
9. one bunch of seedlees black grapes costs $2. how many bunches can you buy for $20?
10. the money used in jordan is called the dinar. the exchange rate is $3 to 2 dinars. find how many dollars you would receive if you exchanged 22 dinars.

Explanation:

Step1: Set up proportion formula

The general formula for proportion problems is $\frac{a}{b}=\frac{c}{d}$, where $a$ and $b$ are the known - quantity pair, and $c$ and $d$ are the unknown - quantity pair. For problems involving cost and quantity, it's $\frac{\text{cost}_1}{\text{quantity}_1}=\frac{\text{cost}_2}{\text{quantity}_2}$.

Problem 1

• Given that one can of pineapple chunks costs $2 (\text{cost}_1 = 2,\text{quantity}_1 = 1)$ and we have $10 (\text{cost}_2 = 10)$. Let the number of cans be $x (\text{quantity}_2=x)$.
• The proportion is $\frac{2}{1}=\frac{10}{x}$.
• Cross - multiply: $2x = 10$.
• Solve for $x$: $x=\frac{10}{2}=5$.

Problem 2

• One jar of crushed ginger costs $2 (\text{cost}_1 = 2,\text{quantity}_1 = 1)$ and we have $4 (\text{cost}_2 = 4)$. Let the number of jars be $x (\text{quantity}_2=x)$.
• The proportion is $\frac{2}{1}=\frac{4}{x}$.
• Cross - multiply: $2x = 4$.
• Solve for $x$: $x = 2$.

Problem 3

• One cantaloupe costs $2 (\text{cost}_1 = 2,\text{quantity}_1 = 1)$ and we have $6 (\text{cost}_2 = 6)$. Let the number of cantaloupes be $x (\text{quantity}_2=x)$.
• The proportion is $\frac{2}{1}=\frac{6}{x}$.
• Cross - multiply: $2x = 6$.
• Solve for $x$: $x = 3$.

Problem 4

• One package of blueberries costs $3 (\text{cost}_1 = 3,\text{quantity}_1 = 1)$ and we have $9 (\text{cost}_2 = 9)$. Let the number of packages be $x (\text{quantity}_2=x)$.
• The proportion is $\frac{3}{1}=\frac{9}{x}$.
• Cross - multiply: $3x = 9$.
• Solve for $x$: $x = 3$.

Problem 5

• The original rectangle has width $w_1 = 24$ and height $h_1 = 12$, and the new height $h_2 = 2$. Let the new width be $w_2$.
• Since the ratio of width to height remains the same, $\frac{w_1}{h_1}=\frac{w_2}{h_2}$.
• Substitute the values: $\frac{24}{12}=\frac{w_2}{2}$.
• Cross - multiply: $12w_2=24\times2$.
• $12w_2 = 48$, so $w_2 = 4$.

Problem 6

• The exchange rate is 6 Tala for $2 (\text{quantity}_1 = 6,\text{cost}_1 = 2)$, and we have $6 (\text{cost}_2 = 6)$. Let the number of Tala be $x (\text{quantity}_2=x)$.
• The proportion is $\frac{6}{2}=\frac{x}{6}$.
• Cross - multiply: $2x=6\times6$.
• $2x = 36$, so $x = 18$.

Problem 7

• Jasmine bought 32 kiwi for $16 (\text{quantity}_1 = 32,\text{cost}_1 = 16)$, and Lisa has $4 (\text{cost}_2 = 4)$. Let the number of kiwi Lisa can buy be $x (\text{quantity}_2=x)$.
• The proportion is $\frac{32}{16}=\frac{x}{4}$.
• Cross - multiply: $16x=32\times4$.
• $16x = 128$, so $x = 8$.

Problem 8

• We can buy 4 bulbs of elephant garlic for $8 (\text{quantity}_1 = 4,\text{cost}_1 = 8)$, and we have $32 (\text{cost}_2 = 32)$. Let the number of bulbs be $x (\text{quantity}_2=x)$.
• The proportion is $\frac{4}{8}=\frac{x}{32}$.
• Cross - multiply: $8x=4\times32$.
• $8x = 128$, so $x = 16$.

Problem 9

• One bunch of seedless black grapes costs $2 (\text{cost}_1 = 2,\text{quantity}_1 = 1)$ and we have $20 (\text{cost}_2 = 20)$. Let the number of bunches be $x (\text{quantity}_2=x)$.
• The proportion is $\frac{2}{1}=\frac{20}{x}$.
• Cross - multiply: $2x = 20$.
• Solve for $x$: $x = 10$.

Problem 10

• The exchange rate is $3$ to 2 Dinars ($\text{cost}_1 = 3,\text{quantity}_1 = 2$), and we have 22 Dinars ($\text{quantity}_2 = 22$). Let the number of dollars be $x (\text{cost}_2=x)$.
• The proportion is $\frac{3}{2}=\frac{x}{22}$.
• Cross - multiply: $2x=3\times22$.
• $2x = 66$, so $x = 33$.

Answer:

1. 5
2. 2
3. 3
4. 3
5. 4
6. 18
7. 8
8. 16
9. 10
10. 33