Question 110537: The sum of two numbers is 76. The second is 8 more than 3 times the first. What are the two numbers? Answer by ptaylor(2198) (Show Source):
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Let x=first number
3x=three times the first
and 3x+8=eight more than three times the first
76-x=the second number
Now we are told the following:
76-x=3x+8 subtract 8 from and also add x to both sides
76-8-x+x=3x+x+8-8 collect like terms
68=4x divide both sides by 4
x=17--------------------first number
76-x=76-17=59----------second number
CK
59+17=76
Also
76-17=3*17+8
59=51+8
59=59
ANOTHER WAY:
Let x=first number
And y=second number
Now we are told the following:
x+y=76---------------------------------eq1
y=3x+8----------------------------------eq2
substitute the value for y from eq2 into eq1 and we have:
x+3x+8=76 subtract 8 from both sides
x+3x+8-8=76-9 collect like terms
4x=68 divide both sides by 4
x=17-----------------------------first number
From eq2:
y=3x+8=3*17+8=59----------------second number
