Question

Helen had $330 in her savings account when Vince opened a savings account with zero dollars. Helen deposited $30 into her account each week for x weeks. Vince deposited $50 into his account each week for x weeks. The accounts did not earn interest. Which inequality represents this situation when the amount of money in Helen's account was greater than the amount of money in Vince's account? A. 30x < 330 + 50x A. , 30x < 330 + 50x B. 50x > 330 + 30x B. , 50x > 330 + 30x C. 30x > 330 + 50x C. , 30x > 330 + 50x D. 50x < 330 + 30x

Answer 1

`50x < 330 + 30x`

Explanation:

Given

Helen:

`Base\ Amount = \$330`

`Weekly = \$30`

Vince:

`Base\ Amount = \$0`

`Weekly = \$50`

First, we need to determine Helen's and Vince's balance at x weeks.

`Balance = Base\ Amount + Weekly\ Earnings * x`

For Helen:

`Balance = 330 + 30 * x`

`Balance = 330 + 30x`

For Vince:

`Balance = 0 + 50 * x`

`Balance = 50x`

As an inequality, we have:

`Helen > Vince`

`330 + 30x > 50x`

Reorder

`50x < 330 + 30x`