Here are the solutions to the problems on the worksheet, using ratio tables.
1. Peanuts Problem
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Goal: Find how many pounds cost $72 if 6 pounds cost $18.
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Step 1: Set up the table with what we know: 6 pounds = $18.
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Step 2: Find the unit rate (cost for 1 pound). Divide both numbers by 6.
* $18 ÷ 6 = $3 per pound.
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Step 3: Find how many pounds you get for $72. Divide the total money by the cost per pound.
* $72 ÷ $3 = 24 pounds.
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Check: 24 pounds × $3/pound = $72. Correct.
2. Map Scale Problem
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Goal: Find the map length in inches if the real road is 1,050 feet long.
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Given: 1 inch on the map = 300 feet in real life.
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Step 1: Set up the ratio: 1 inch / 300 feet.
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Step 2: We need to find out how many groups of 300 are in 1,050.
* 1,050 ÷ 300 = 3.5
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Step 3: Since there are 3.5 groups of 300 feet, the map length is 3.5 inches.
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Check: 3.5 inches × 300 feet/inch = 1,050 feet. Correct.
3. Sugar Cookies Problem
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Goal: Find cups of sugar for 72 cookies.
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Given: 3 cups make 48 cookies.
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Step 1: Simplify the ratio. Both 3 and 48 can be divided by 3? No, let's divide by common factors. Let's try dividing by 12.
* 48 ÷ 12 = 4 cookies.
* 3 ÷ 12 = 0.25 cups. This is messy.
* Let's find the amount of sugar for 1 cookie first? Or simplify differently.
* Let's divide 48 by 16 to get 3 cookies? No.
* Let's just use cross-multiplication logic via a table.
* Row 1: 3 cups | 48 cookies
* Divide both by 3: 1 cup | 16 cookies. (Because 48 ÷ 3 = 16).
* So, 1 cup of sugar makes 16 cookies.
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Step 2: How many cups for 72 cookies?
* 72 ÷ 16 = 4.5
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Answer: 4.5 cups.
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Check: 4.5 cups × 16 cookies/cup = 72 cookies. Correct.
4. Soda Cost Problem
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Goal: Find cost for 9 cartons if 2 cartons cost $4.96.
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Step 1: Find the cost of 1 carton.
* $4.96 ÷ 2 = $2.48 per carton.
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Step 2: Multiply by 9 cartons.
* $2.48 × 9
* 2 × 9 = 18
* 0.48 × 9 = 4.32
* 18 + 4.32 = $22.32
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Check: $22.32 ÷ 9 = $2.48. $2.48 × 2 = $4.96. Correct.
5. Inches to Feet Problem
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Goal: Convert 16 feet to inches.
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Given: 96 inches = 8 feet.
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Step 1: Find how many inches are in 1 foot.
* 96 ÷ 8 = 12 inches per foot.
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Step 2: Calculate inches in 16 feet.
* 16 × 12
* 10 × 12 = 120
* 6 × 12 = 72
* 120 + 72 = 192 inches.
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Alternative Check: 16 feet is exactly double 8 feet. So, double the inches: 96 × 2 = 192. Correct.
Final Answer:
1. 24 pounds
2. 3.5 inches
3. 4.5 cups
4. $22.32
5. 192 inches
Parent Tip: Review the logic above to help your child master the concept of ratio tables math.
