Question 627338

the difference between two multiples of 10 is 330 and their sum is 710.find the numbers


Let the larger and smaller multiplicative factors of the two multiples be L and S, respectively
Then the multiples are 10L & 10S, and since their difference is 330, we have: 10L - 10S = 330 ---- 10(L) - 10(S) = 10(33)
L – S = 33 ------- eq (i)
Also, 10L + 10S = 710 ------ 10(L) + 10(S) = 10(71)
L + S = 71 ----- eq (ii)
L – S = 33 ------- eq (i)
2L = 104 ------ Adding eqs (i) and (ii) 
L, or larger multiplicative factor = 104/2, or 52, which means that the larger multiple is 10(52), or {{{highlight_green(520)}}}


52 – S = 33 ------ Substituting 52 for L in eq (i) 
- S = 33 – 52
S, or smaller multiplicative factor = {{{(- 19)/- 1}}}, or 19, which means that the smaller multiple is 10(19), or {{{highlight_green(190)}}} 


You can do the check, I'm sure!!


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