NavGanitMateby NavGreen Compute, AustraliaBased on Victorian Curriculum Mathematics v2.0
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Fractions and recurring decimals

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A school in Brisbane orders 13 science kits and 64 art kits for a new program. The total cost for all kits is $1248.00.

Each science kit costs $16.00 and each art kit costs $12.00. What is the exact fraction of the total cost that is attributed to the art kits?

Express your answer as a simplified fraction.

Concept illustrations

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Half in three forms. 1/2 = 0.5 = 50%. The whole is divided into two equal parts.1 of 2 equal parts
1/2 = 0.5 = 50%. The whole is divided into two equal parts.
Common denominators as equal strips. The first strip selects 4/12 = 1/3; the second selects 3/12 = 1/4. The result selects 7/12. Every strip represents the same whole.1/31/47/124/12 + 3/12 = 7/12
The first strip selects 4/12 = 1/3; the second selects 3/12 = 1/4. The result selects 7/12. Every strip represents the same whole.

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The total cost for 13 science kits and 64 art kits is $1248.00. Each science kit costs $16.00 and each art kit costs $12.00. We are to find the fraction of the total cost that comes from art kits.
  2. Calculate the total cost of science kits: 13 kits × $16.00 per kit = $208.00.
  3. Subtract the science kit cost from the total to find the art kit cost: $1248.00 - $208.00 = $1040.00.
  4. The total cost is $1248.00 and the art kit cost is $1040.00. The fraction of the total cost from art kits is $1040.00 / $1248.00.
  5. Simplify the fraction 1040/1248 by dividing both numerator and denominator by their greatest common divisor (GCD). First, factor both numbers.
  6. Factor 1040: 1040 = 16 × 65 = 2^4 × 5 × 13.
  7. Factor 1248: 1248 = 16 × 78 = 2^4 × 6 × 13 = 2^4 × 2 × 3 × 13 = 2^5 × 3 × 13.
  8. The common factors are 2^4 and 13. So GCD = 2^4 × 13 = 16 × 13 = 208.
  9. Divide numerator and denominator by 208: 1040 ÷ 208 = 5, 1248 ÷ 208 = 6. So the simplified fraction is 5/6.
  10. Check: 5/6 of $1248.00 = (5 × 1248) / 6 = 6240 / 6 = $1040.00. This matches the art kit cost.
  11. The fraction of the total cost attributed to art kits is exactly 5/6.
  12. The answer is 5/6, which is a simplified fraction and matches the required format.

Reference answer: 5/6

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