Question

Hi, for the question, "the sum of two numbers is equal to a third number(x+y=z). The sum of twice the first, three times the second, and twice the third is 7(2x+3y+2x=7). The third number is 3 more than the first(3+z=x), have I set the equations right? I got different answers than my book that still satisfy all the equations.

Answer 1

looks like you did this ..
first no ---- x
second no -- y
third no ----x+y

now... " The sum of twice the first, three times the second, and twice the third is 7"
2x + 3y + 2(x+y) = 7
2x + 3y + 2x + 2y = 7
4x + 5y = 7 (#1)

also ... "The third number is 3 more than the first"
x+y = x+3
y = 3

back in #1
4x + 5(3) = 7
4x + 15 = 7
4x = -8
x = -2

first no -- -2
2nd no -- 3
3rd no -- 1

Check:
is the third the sum of the first two ? YEAH
is twice the first plus three times the second and twice the third is 7 ?
(-4 + 9 + 2 = 7 YEAH)
is the third 3 more than the first ?
1 is indeed 3 more than -2
YEAHHH

Answer 2

Dear Reiny! U r a life-saver! Is there a short cut to how can I set the question or change word problems into math one? It seems that this is my problem! Also, why did my way worked as well with different answers? My answers satisfied all equations as well. Many thanks.