Writing and solving equations and systems

Question

Bryce started the year with $435 in the bank and is saving $25 per week Wade started the year with $875 and is spending $15 per week right a system of equations for these two boys then figure out when they will have the same amount of money.

Answer 1

For Bryce, he started the year with $435 in the bank. Since he is adding $25 per week, after the first week he has 435 + 25. Then after the second week he has that amount plus another $25. So, to calculate the amount he has at any particular time add $435 and $25 multiplied by the number of weeks or:

B = 435 + 25t (where "B" is the amount Bryce has in the bank and "t" is the time gone by (number of weeks).

For Wade, using the same idea, we get:

W = 875 - 15t (notice we have to subtract because he is spending money while Bryce was saving).

System of equations:

B = 435 + 25t

W = 875 - 15t

But, we are told one more thing, we are trying to find the time when their bank accounts are the same. So we can just call the money in the bank by a single variable since B = W. That means the system of equations becomes:

B = 435 + 25t

B = 875 - 15t

This means:

435 + 25t = 875 - 15t

Subtract 435 from both sides to get:

25t = 440 - 15t

Add 15 t to both sides to get:

40t = 440

Divide both sides by 40 to get:

t = 11

After 11 weeks, their bank accounts will both have the same amount. To know how much that is, you can plug t = 11 into either equation.