nezukochan234
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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?

Sagot :

VirαtKσhli

Answer:

[tex]\large{\boxed{\sf x = 30 , \ y \ = \ 20}}[/tex]

Step-by-step 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 ,

[tex]\sf\qquad\longrightarrow x + y = 50.....(i)[/tex]

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

[tex]\sf\qquad\longrightarrow 2x + 5y = 160 ..... (ii) [/tex]

Multiply equation (i) with 5 ,

[tex]\sf\qquad\longrightarrow 5x + 5y = 250 [/tex]

Subtract equation (ii) and (i) ,

[tex]\sf\qquad\longrightarrow 5x - 2x = 250-160\\[/tex]

[tex]\sf\qquad\longrightarrow 3x = 90\\[/tex]

[tex]\sf\qquad\longrightarrow x =\dfrac{90}{3}\\[/tex]

[tex]\sf\qquad\longrightarrow \pink{ x = 30} [/tex]

Substitute this value in (i) ,

[tex]\sf\qquad\longrightarrow y = 50-x \\ [/tex]

[tex]\sf\qquad\longrightarrow y= 50-30\\ [/tex]

[tex]\sf\qquad\longrightarrow \pink{ y = 20} [/tex]

Hence ,

  • No. of 2 point question = 30
  • No. of 5 point question = 20
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