Multiple choice

A farmer sold a calf and a cow for \$760, thereby making a profit of 25% on the calf and 10% on the cow. By selling them for \$767.50, he would have realised a profit of 10% on the calf and 25% on the cow. What was the cost price of the cow?

  1. $300
  2. $250
  3. $400
  4. $350
  5. $200
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let C be cost of calf, W be cost of cow. 1.25C + 1.10W = 760 and 1.10C + 1.25W = 767.50. Adding equations: 2.35(C+W) = 1527.5, C+W = 650. Subtracting: 0.15W - 0.15C = 7.5, W - C = 50. Solving C+W=650 and W-C=50 gives W=350, C=300.

AI explanation

Let the cost price of the calf be C and the cow be W. The equations are 1.25C plus 1.10W = 760 and 1.10C plus 1.25W = 767.50. Multiplying the first equation by 1.25 and the second by 1.10, then subtracting yields 0.2025W = 70.875. Solving this gives the cost price of the cow as 350.

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