Question 165142
Let S = smaller number
and
L = larger number
.
Since we have two unknowns, we'll need two equations.
.
Equation 1: "five times the larger plus three times the smaller is 47"
5L + 3S = 47
.
Equation 2: "four times the larger minus twice the smaller is 20"
4L - 2S = 20
.
Using the "substitution method", solve equation 2 for S:
4L - 2S = 20
4L = 2S + 20
4L-20 = 2S
2L-10 = S
.
Substitute the above into equation 1 and solve for L:
5L + 3S = 47
5L + 3(2L-10) = 47
5L + 6L-30 = 47
11L - 30 = 47
11L = 77
L = 7
.
Finally, plug the above back into equation 2 and solve for S:
4L - 2S = 2
4(7) - 2S = 2
28 - S = 1
28 = S + 1
27 = S
.
Solution: The two numbers are 7 and 27