Question

Two runners are saving money to attend a marathon. the first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. the second runner has $50 in savings and will save $60 each month. which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money? 112 – 25m 45 = 50 – 60m 112 25 45m = 50m 60 112 25 – 45m = –50m 60 112 25m 45 = 50 60m

Answer 1

The equation that we need to solve is:

$157 + $50*m = $50 + $60*m

And the solution is m = 10.7 months.

Which equation models the situation?

For the first runer we have a initial amount of $112 + $45 = $157 plus $50 per month, so we can write:

f(m) = $157 + $50*m

And the second runner has an initial amount of $50 and saves $60 per month, so we can write the linear equation:

g(x) = $50 + $60*m

They will have the same amount of money when:

f(x) = g(x)

$157 + $50*m = $50 + $60*m

$107 = $10*m

$107/$10 = m = 10.7

So, after 10.7 months, both accounts will have the same money.

If you want to learn more about linear equations:

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