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The average of two numbers is 10. Thrice the smaller number is equal to          twice the larger number. What is one more than the larger number? 1 pointA. 8B. 9C. 12D. 13

Question

The average of two numbers is 10. Thrice the smaller number is equal to          twice the larger number. What is one more than the larger number? 1 pointA. 8B. 9C. 12D. 13

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Solution

Let's denote the smaller number as x and the larger number as y.

From the problem, we have two equations:

  1. The average of two numbers is 10, so (x + y) / 2 = 10. Multiply both sides by 2 to get x + y = 20.

  2. Thrice the smaller number is equal to twice the larger number, so 3x = 2y.

We can solve these two equations simultaneously.

From the second equation, we can express y in terms of x: y = 3x / 2.

Substitute y = 3x / 2 into the first equation: x + 3x / 2 = 20. Multiply all terms by 2 to get rid of the denominator: 2x + 3x = 40. Combine like terms to get 5x = 40. Divide both sides by 5 to solve for x: x = 8.

Substitute x = 8 into the equation y = 3x / 2 to find y: y = 3 * 8 / 2 = 12.

So, the larger number is 12. One more than the larger number is 12 + 1 = 13.

Therefore, the answer is D. 13.

This problem has been solved

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