Question

A test has twenty questions worth 100 points. The test consists of x true-false questions worth 4 points each and y multiple choice questions worth 8 points each. How many of each type of question are on the test?

Answer 1

Answer:

Number of true-false questions  =15

Number of multiple choice questions  =5

Step-by-step explanation:

Number of true-false questions  =$x$

Number of multiple choice questions  =$y$

Total number of question =$x+y=20$

Points for true-false questions = 4

Total points for true-false questions = $4\times x =4x$

Points for multiple choice questions = 8

Total points for multiple choice questions = $8\times y =8y$

Total points of the test = $4x+8y=100$

We have 2 equations now:

(1) $x+y=20$

(2) $4x+8y=100$

We need to solve the 2 equations to find $x$ and $y$.

Dividing equation 2 by 4.

$\frac{4x+8y}{4}=\frac{100}{4}$

(2a) $x+2y=25$

Multiplying equation (2a) with (-1)

$-1(x+2y)=25\times (-1)$

(2b) $-x-2y=-25$

Adding equation (2a) with equation (1).

$x+y=20$

$-x-2y=-25$

$-y=-5$

$y=5$      [ Divided both sides by -1]

Substituting value of $y$ in equation (1).

$x+5=20$

Subtracting both sides by 5.

$x+5-5=20-5$

$x=15$

∴$x=15 \ and\ y=5$

Number of true-false questions  =15

Number of multiple choice questions  =5

Answer 2

Answer:

1: 15

2: 5

Step-by-step explanation: