Brandon took a 50-question exam worth a total of 160 points. There were x two-point questions and y five point questions. How many of each type of question were on the exam?

Question

asked Apr 25, 2023 88.4k views

1 Answer

Gringo · Answer 1 · 2023-04-28T15:20:59+0000

Answer:

$\large{\boxed{\sf x = 30 , \ y \ = \ 20}}$

Explanation:

Here it is given that Brandon took a 50 question exam worth of 160points . So here the sum of 2 point and 5 point question is 50. So ,

$\sf\qquad\longrightarrow x + y = 50.....(i)$

Again the maximum marks for the exam is 160 . Therefore ,

$\sf\qquad\longrightarrow 2x + 5y = 160 ..... (ii)$

Multiply equation (i) with 5 ,

$\sf\qquad\longrightarrow 5x + 5y = 250$

Subtract equation (ii) and (i) ,

$\sf\qquad\longrightarrow 5x - 2x = 250-160\\$

$\sf\qquad\longrightarrow 3x = 90\\$

$\sf\qquad\longrightarrow x =(90)/(3)\\$

$\sf\qquad\longrightarrow \pink{ x = 30}$

Substitute this value in (i) ,

$\sf\qquad\longrightarrow y = 50-x \\$

$\sf\qquad\longrightarrow y= 50-30\\$

$\sf\qquad\longrightarrow \pink{ y = 20}$

Hence ,