word problem

Apr 2016
15
0
canada
A test has 20 questions worth a total of 100 marks. There are two types of questions on this test. There are T/F questions worth 4 marks each, and short-answer questions worth 8 marks each. How many of each type are there?

so far what i got is:

x= t/f questions
y= short answer

4x+8y = 100
x + y = 20

i was wondering if i got this system of equation right?
 

romsek

MHF Helper
Nov 2013
6,828
3,073
California
yes it's right
 
Sep 2016
84
19
India
yes!
Now, you can find it easily.
4x+8y = 100........(1)
x + y = 20...........(2)
Now, multiply equation(2) by 4
4x+4y = 80...........(3)
Subtract equ(3) from (1)

4x+8y = 100
-4x -4y = -80
-------------------
4y =20
y =5
Put the value of y in equ(2)
x+5 =20
x =15
Thus. x=15 and y=5