Question

what sentence represent the number of poins in the problem below

Answer 1

hello

to solve this question, we can write out two sets of equation and solve them

let the short answers be represented by x

let the multiple-choice questions be represented by y

we know that the test has 60 points

multiple-choice carries 2 points

short answers carries 5 points

$2x+5y=60$

now we have a total of 15 questions which comprises of multiple-choice questions and short answers

$x+y=15$

now we have two set of equations which are

$\begin{gathered} 2x+5y=60\ldots\text{equ}1 \\ x+y=15\ldots\text{equ}2 \end{gathered}$

now let's solve for x and y

from equation 2, let's make x the subject of formula

$\begin{gathered} x+y=15 \\ x=15-y\ldots\text{equ}3 \end{gathered}$

put equation 3 into equation 1

$\begin{gathered} 2x+5y=60 \\ x=15-y \\ 2(15-y)+5y=60 \\ 30-2y+5y=60 \\ 30+3y=60 \\ \text{collect like terms} \\ 3y=60-30 \\ 3y=30 \\ \text{divide both sides by the coeffiecient of y} \\ \frac{3y}{3}=\frac{30}{3} \\ y=10 \end{gathered}$

now we know the value of y which is the number of multiple-choice question. we can use this information to find the number of short answer through either equation 1 or 2

from equation 2

$\begin{gathered} x+y=15 \\ y=10 \\ x+10=15 \\ \text{collect like terms} \\ x=15-10 \\ x=5 \end{gathered}$

from the calculations above, the number of short answers is equal to 5 and multiple-choice questions is equal to 10.

The answer to this question is option C