Question

A school basketball team has an expense account and a fundraising account. After tt weeks, the balance of the expense account is (400−40t)(400−40t) dollars and the balance of the fundraising account is (150+32t)(150+32t) dollars.

a. Write an expression in simplest form that represents the total amount (in dollars) in both accounts after tt weeks.

An expression is (

550−72t) dollars.


b. What is the total amount (in dollars) in both accounts after 12 weeks?


Amount after 12 weeks: $

Answer 1

a. 550-8t

b. 454 dollars

Explanation:

a. Calling t the number of weeks, the balance in the first account is

(400-40t)(400−40t)

while the balance in the second account is

(150+32t)(150+32t)

So, the total amount in both accounts is the sum of the balances of the two accounts:

(400-40t)+(150+32t)=(400+150)+(-40t+32t)=550-8t(400−40t)+(150+32t)=(400+150)+(−40t+32t)=550−8t

b. To find the total amount in both accounts after 12 weeks, we just need to substitute t=12 into the total balance, and we find:

550-8t=550-8\cdot 12=550-96=454550−8t=550−8⋅12=550−96=454

Answer 2

a. 550-8t

b. 454 dollars

Explanation:

a. Calling t the number of weeks, the balance in the first account is

`(400-40t)`

while the balance in the second account is

`(150+32t)`

So, the total amount in both accounts is the sum of the balances of the two accounts:

`(400-40t)+(150+32t)=(400+150)+(-40t+32t)=550-8t`

b. To find the total amount in both accounts after 12 weeks, we just need to substitute t=12 into the total balance, and we find:

`550-8t=550-8\cdot 12=550-96=454`