SOLUTION: I am thinking of 2 numbers. Three times the first added to four times the second is 65, while four times the first added to three times the second is 61. What is the sum of the two

Question 1011638: I am thinking of 2 numbers. Three times the first added to four times the second is 65, while four times the first added to three times the second is 61. What is the sum of the two numbers?
Found 2 solutions by ankor@dixie-net.com, Cromlix:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write an equation for each statement
:
I am thinking of 2 numbers.
a & b
Three times the first added to four times the second is 65,
3a + 4b = 65
while four times the first added to three times the second is 61.
4a + 3b = 61
:
multiply the 1st equation by 4, the 2nd equation by 3
12a + 16b = 260
12a + 9b = 183
------------------Subtraction eliminates a, find b
7b = 77
b = 77/7
b = 11
Find a using the 1st equation, replace b with 11
3a + 4(11) = 65
3a = 65 - 44
3a = 21
a = 21/3
a = 7
:
What is the sum of the two numbers? 7 + 11 = 18
:
;
Check our solutions in the 2nd equation
4(7) + 3(11) = 61
28 + 33 = 61
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
Three times the first added to four
times the second is 65.
3x + 4y = 65......(1)
while four times the first added to
three times the second is 61.
4x + 3y = 61......(2)
.................
3x + 4y = 65......(1)
4x + 3y = 61......(2)
Multiply (1) by 4
Multiply (2) by 3
12x + 16y = 260......(1)
12x + 9y = 183......(2)
Subtract (2) from (1)
.....7y = 77
......y = 11
Substitute y = 11 into (1)
3x + 4y = 65......(1)
3x + 4(11) = 65
3x + 44 = 65
3x = 65 - 44
3x = 21
x = 7
First number = 7
Second number = 11
Hope this helps :-)
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