Question

Allan and Dave bowl together and their combined total score for one game was 375 points. Allan’s score was 60 less than twice Dave’s. What were their scores?

Which is a system of equations to model the problem if x represents Dave’s score and y represents Allan’s score?

A. x + y = 60
y = 2x – 375

B. x + y = 375
y = 2x – 60

C. x + y = 375
y = 2x + 60

D. x – y = 375
y = 2x – 60

Answer 1

B. x + y = 375

y = 2x – 60

Explanation:

Given :Allan and Dave bowl together and their combined total score for one game was 375 points. Allan’s score was 60 less than twice Dave’s.

To Find:

What were their scores?

Which is a system of equations to model the problem if x represents Dave’s score and y represents Allan’s score?

Solution :

x repesents Dave’s score

y represents Allan’s score

Since we are given that their combined total score for one game was 375 points

⇒x+y=375 ---1

Now we are given that Allan’s score was 60 less than twice Dave’s

⇒y =2x-60---2

Thus x+y=375 and y =2x-60 is a required system of equations.

So, option b is correct.

Now to calculate their scores.

Put value of y from equation 2 in 1

⇒x+(2x-60)=375

⇒3x=375+60

⇒3x=435

⇒
`x =(435)/(3)`

⇒x=145

Now put this value of x in equation 1 to get value of y

⇒145+y=375

⇒y=375-145

⇒y=230

Thus Dave's score is 145 and Allan's score is 230

Answer 2

A system of equations is:
B )
x + y = 375
x = 2 y - 60
We will solve this system:
2 y - 60 + y = 375
3 y = 435
y = 435 : 3
y = 145
x = 375 - 145
x = 230
Allan`s score was 230 and Dave`s score was 145.