# 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 $\displaystyle x=$number of 5 point problems
then you let $\displaystyle y=$the number of two point problems

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

and

$\displaystyle 5x+2y=100$

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

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

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