The sum of two numbers is 63. One number is five less than three times the other. What's the answer?

1 Answer
Jun 29, 2018

#17 and 46#

Explanation:

Turn each of the phrases into math equations, and then solve. Since there are two numbers, I will call one #x# and the other #y#.

#stackrel(x + y)overbrace"The sum of two numbers"stackrel(=)overbrace"is"stackrel(63)overbrace"63"#

#stackrel(x)overbrace"one number"stackrel(=)overbrace"is"stackrel(3y - 5)overbrace"five less than three times the other"#

#x +y = 63#

#x = 3y - 5#

Substitute the second equation into the first one:

#x + y = 63#

#(3y - 5) + y = 63#

#3y - 5 + y = 63#

#4y - 5 = 63#

#4y = 68#

#y = 17#

Now substitute the value for #y# into one of the equations and solve:

#x = 3y - 5#

#x = 3(17) -5#

#x = 51 - 5#

#x = 46#

So the two numbers are #17# and #46#.