Question

You and your friend are having a contest to see who can earn more homework passes in your favorite class, Math. At the end of the year, you earned 4 more homework passes

than your friend. Together, you and your friend earn 24 homework passes. Write a
system of linear equations that represents this situation. How many homework passes do
each of you earn?

Answer 1

The number of homework passes earn by me is 14

The number of homework passes earn by friend is 10

Explanation:

Given as :

The number of homework passes earn by me = 4 + number of homework passes earn by friend

And

The number of homework passes earn by me + number of homework passes earn by friend = 24

Let The number of homework passes earn by friend = f

So, The number of homework passes earn by me = m = 4 + f

i.e m = 4 + f

Or, m - f = 4 ............A

And

m + f = 24 .............B

Now, Solving eq A and eq B

(m - f) + (m + f) = 4 + 24

Or, ( m + m ) + (- f + f ) = 28

Or, 2 m + 0 = 28

∴ m =
`(28)/(2)`

i.e m = 14

So, The number of homework passes earn by me = m = 14

Now, Put the value of m into eq A

∵ m - f = 4

Or, f = m - 4

Or, f = 14 - 4

i.e f = 10

So, The number of homework passes earn by friend = f = 10

Hence, The number of homework passes earn by me is 14 and

The number of homework passes earn by friend is 10 Answer