SOLUTION: Hi, I need help on getting this answer - Three times the larger of 2 numbers increased by 4 times the smaller is 205. Six times the larger plus 3 times the smaller is 270. Find the

Question 76252: Hi, I need help on getting this answer - Three times the larger of 2 numbers increased by 4 times the smaller is 205. Six times the larger plus 3 times the smaller is 270. Find the numbers.
Thank you
Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
Let larger number = x and smaller number = y.
Three times the larger number (= 3x) increased by 4 times the smaller = 3x + 4y.
This value is given 205.
So, 3x + 4y = 205 __________(1)

Six times the larger number (= 6x) plus 3 times the smaller = 6x + 3y.
This value is given 270.
So, 6x + 3y = 270
or 2x + y = 90 ___________(2)
We now have to solve equations (1) and (2) to find x and y.
Multiplying both sides of eq (2) with 4 and subtracting both sides of eq (1) from it
4(2x + y) - (3x + 4y) = 4*90 - 205
(8x + 4y) - (3x + 4y) = 360 - 205
5x = 155
x = 31
So from (2)
2*31 + y = 90
or y = 90 - 62 = 28
Thus the numbers are 31 and 28.
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