Question

If x and y vary directly, and y is 56 when x is 8, find y when x is 5.

a) 35
b) 70
c) 45
d) 28

Answer 1

Using the formula for direct variation, the constant of variation (k) is found to be 7. When x is 5, the value of y is calculated to be 35. Therefore, the correct answer is a) 35.

Step-by-step explanation:

If x and y vary directly, it means that when one variable increases, the other increases at a constant rate, and vice versa. This relationship can be expressed with the formula y = kx, where k is the constant of variation. To find k, you use the values given in the question:

• Given that y = 56 when x = 8, we can find k by rearranging the formula to k = y/x. So k = 56/8 = 7.
• Now that we know k, we can find y when x = 5 by substituting these values into the formula: y = 7 * 5 = 35.

Therefore, when x is 5, y is 35. The correct answer is a) 35.