Problem: Two numbers are such that their difference, their sum, and their product are to one another as 1:7:24. The product of the two numbers is:
Answer Choices:
A. 6
B. 12
C. 24
D. 48
E. 96
Solution:
Let the numbers be represented by x and y. Then x+y=7(x−y) and xy=24(x−y). Therefore. 8y=6x and xy=24x−24y=24x−18x=6x
∴x(y−6)=0. The value x=0 is not usable, so that y=6. Since 6x=8y,x=8∴xy=48.