SOLUTION: the sum of two numbers is 50. Two times the smaller number exceeds the larger number by 31. Find the numbers.

Question 600129: the sum of two numbers is 50. Two times the smaller number exceeds the larger number by 31. Find the numbers.
Answer by godsgirls(5) (Show Source): You can put this solution on YOUR website!
The sum of two numbers is 50. Two times the smaller number exceeds the larger number by 31. Find the numbers.
First we need to write out equations. Let x equal the first number and y equal the second. The sum of two numbers is 50:
Two times the smaller number (we'll make that x) exceeds the larger number (y) by 31.
Here I'm going to teach you a trick that will become handy once you get into high school math.
It's called combining equations.
First we need to multiply the first equation by 2.
becomes
of course, we know from our second equation that 2x = y + 31. So we substitute this into our first equation.

Combine like terms to get:
subtract 31 from each side:
Simplify:
divide both sides by three to isolate y.
this becomes:
Now we have y, we can use our first equation to find x.

substitute 23 for y:
subtract 23 from each side.
simplify:
So your two numbers are 27 and 23. I hope this helps you!

RELATED QUESTIONS
the sum of two numbers is 50. two times the smaller number exceeds the larger number by... (answered by Fombitz)

the sum of two numbers is 50. two times the smaller number exceeds the larger number by... (answered by josgarithmetic)

The sum of two numbers is 50. Two times the smaller number exceeds the larger number by... (answered by stanbon)

the sum of two numbers is 85. Two times the smaller number exceeds the larger number... (answered by rothauserc)

The sum of two numbers is 50. The larger exceeds the smaller by 22. What is the larger... (answered by JulietG)

the sum of two numbers is 73. five times the smaller number exceeds the larger number by... (answered by oberobic)

the sum of two numbers is 38. three times the smaller number exceeds the larger number by (answered by nerdybill,biancafranco86)

the sum of two numbers is 38. three times the smaller number exceeds the larger number by (answered by 55305)

The sum of two numbers is 38. Four times the smaller exceeds three times the larger... (answered by flame8855)