Here are the step-by-step solutions for each problem on the worksheet.
Problem 1
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Step 1: Identify the ratio and the known value. The ratio of Father's height to Son's height is $3:2$. The son's height is $116$ cm.
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Step 2: Set up the relationship. Since the ratio is $3:2$, we can say:
$$\frac{\text{Father}}{\text{Son}} = \frac{3}{2}$$
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Step 3: Substitute the son's height into the equation:
$$\frac{\text{Father}}{116} = \frac{3}{2}$$
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Step 4: Solve for the father's height. First, find the value of one "part" by dividing the son's height by his ratio number ($2$):
$$116 \div 2 = 58$$
So, one part equals $58$ cm.
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Step 5: Multiply that value by the father's ratio number ($3$):
$$58 \times 3 = 174$$
Problem 2
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Step 1: Identify the numbers. There are $20$ cars and $80$ wheels.
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Step 2: Write the ratio as requested (cars to wheels):
$$20 : 80$$
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Step 3: Simplify the ratio. Both numbers end in $0$, so we can divide both by $10$:
$$2 : 8$$
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Step 4: Both numbers are even, so divide by $2$:
$$1 : 4$$
Problem 3
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Step 1: Identify the ratio and the known value. The ratio of Girls to Boys is $5:4$. There are $32$ boys.
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Step 2: Find the value of one "part". The boys represent the "$4$" in the ratio. Divide the total number of boys by $4$:
$$32 \div 4 = 8$$
So, one part equals $8$ students.
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Step 3: Calculate the number of girls. The girls represent the "$5$" in the ratio. Multiply the value of one part by $5$:
$$8 \times 5 = 40$$
Problem 4
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Step 1: Identify the numbers. Mary received $120$ e-mails and answered $60$.
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Step 2: Write the ratio as requested (received to answered):
$$120 : 60$$
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Step 3: Simplify the ratio. Divide both numbers by $60$:
$$120 \div 60 = 2$$
$$60 \div 60 = 1$$
The ratio is $2:1$.
Problem 5
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Step 1: Identify the rate. The bakery gives $6$ pastries for every $5$ cookie packets.
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Step 2: Determine how many groups of "5 cookie packets" are in the purchase of $30$ packets.
$$30 \div 5 = 6 \text{ groups}$$
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Step 3: Calculate the total pastries. Since there are $6$ groups, and each group gets $6$ pastries, multiply:
$$6 \text{ groups} \times 6 \text{ pastries} = 36 \text{ pastries}$$
Final Answer:
1) 174 cm
2) 1:4
3) 40 girls
4) 2:1
5) 36 pastries
Parent Tip: Review the logic above to help your child master the concept of trig ratios word problems worksheet.
