# Thread: can you help me with this word problem

1. ## can you help me with this word problem

38 problems on a test worth a total of 100 points.
each test problem is either worth 5 points or 2 points .
how many 5 point questions and 2 point questions

2. Originally Posted by dblued
38 problems on a test worth a total of 100 points.
each test problem is either worth 5 points or 2 points .
how many 5 point questions and 2 point questions
Solve simutaneously:
x + y = 38
5x + 2y = 100.

okay, so you let $x=$number of 5 point problems
then you let $y=$the number of two point problems

since you have two variables you need two equations that are related
$x+y=38$

and

$5x+2y=100$

then you can say that $y=38-x$ and you can substitute that value in for y, so

$5x+2(38-x)=100$
$5x+(76-2x)=100$
$3x=24$ and $x=8$

then solve for y
$x+y=38$
$8+y=38$
$y=30$