Here are the step-by-step solutions for each problem on the worksheet.
1 a.
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Step 1: The ratio of pinto beans to black beans is $1 : 1$. This means for every 1 pinto bean, there is 1 black bean. They are equal in number.
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Step 2: We know there are 300 pinto beans. Because the ratio is $1:1$, there must also be 300 black beans.
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Step 3: To find the total, add them together: $300 + 300 = 600$.
2 a.
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Step 1: The reward is shared in a ratio of $2 : 5$ (Jayden : Caden).
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Step 2: Add the parts of the ratio together to find the total number of "shares": $2 + 5 = 7$ total shares.
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Step 3: Jayden gets 2 of those shares. So, his fraction of the total is $\frac{2}{7}$.
*(Note: You don't need to calculate the dollar amount to answer what fraction he gets, but if you did, it would be $\frac{2}{7}$ of $\$140$, which is $\$40$.)*
3 a.
*
Step 1: The ratio of nickels : dimes : quarters is $8 : 1 : 2$.
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Step 2: We are told there are 30 quarters. In the ratio, quarters represent the "2" part.
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Step 3: Find the value of one "part" by dividing the number of quarters by their ratio number: $30 \div 2 = 15$. So, 1 part equals 15 coins.
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Step 4: Calculate Nickels (8 parts): $8 \times 15 = 120$ nickels.
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Step 5: Calculate Dimes (1 part): $1 \times 15 = 15$ dimes.
4 a.
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Step 1: The ratio of girls to boys is $2 : 4$. This can be simplified to $1 : 2$, but we can work with the original numbers too.
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Step 2: There are 14 girls. The "girls" part of the ratio is 2.
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Step 3: Find the value of one part: $14 \div 2 = 7$. So, 1 part equals 7 people.
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Step 4: Find the number of boys (4 parts): $4 \times 7 = 28$ boys.
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Step 5: Find the total members by adding girls and boys: $14 + 28 = 42$.
5 a.
*
Step 1: Total beans = 550. White beans are $\frac{2}{5}$ of the total.
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Step 2: Calculate the number of white beans: $\frac{2}{5} \times 550$. First, $550 \div 5 = 110$. Then, $110 \times 2 = 220$ white beans.
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Step 3: Calculate the number of navy beans (the rest): $550 - 220 = 330$ navy beans.
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Step 4: Write the ratio of white to navy: $220 : 330$.
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Step 5: Simplify the ratio. Both numbers end in 0, so divide by 10: $22 : 33$. Both are divisible by 11.
* $22 \div 11 = 2$
* $33 \div 11 = 3$
* The simplified ratio is $2 : 3$.
6 a.
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Step 1: The reward is shared in a ratio of $1 : 8$ (Sophia : Isabella).
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Step 2: Add the parts of the ratio together to find the total shares: $1 + 8 = 9$ total shares.
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Step 3: Sophia gets 1 of those shares. So, her fraction of the total is $\frac{1}{9}$.
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Final Answer:
1 a. 600 beans
2 a. 2/7
3 a. 120 nickels and 15 dimes
4 a. 42 members
5 a. 2 : 3
6 a. 1/9
Parent Tip: Review the logic above to help your child master the concept of ratio word problems worksheet 7th grade.
