SOLUTION: Susan has a $100 gift card to her favorite restaurant. Each day, she uses her gift card to buy the same lunch for $8.50. Bret has a $75 gift card to the same restaurant. His lunche

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Question 1151784: Susan has a $100 gift card to her favorite restaurant. Each day, she uses her gift card to buy the same lunch for $8.50. Bret has a $75 gift card to the same restaurant. His lunches cost $6 each. Write an inequality to find what number of lunches Susan’s gift card balance will be greater than Bret’s gift card balance.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
her balance is equal to 100 - 8.50 * x
his balance is equal to 75 - 6.00 * x
x is the number of lunches.

her balance will be greater than his when 100 - 8.50 * x > 75 - 6.00 * x.

subtract 75 from both sides of this inequality and add 8.50 to both sides of this inequality to get:
100 - 75 > 8.50 * x - 6.00 * x
combine like terms to get:
25 > 2.50 * x
divide both sides of this inequality by 2.5 to get:
25 / 2.5 > x
simplify to get:
10 > x
if 10 is greater than x, than x must be smaller than 10, therefore the inequality can be written as:
x < 10

her balance is greater than his as long as the number of lunches is less than 10.
their balance will be equal when x = 10.
his balance will be greater than her when x > 10

for example:

when x = 5:
her balance is 100 - 8.50 * 5 = 57.5
his balance is 75 - 6.00 * 5 = 45
her balance is greater.

when x = 11:
her balance is 100 - 8.50 * 11 = 6.5
his balance is 75 - 6.00 * 11 = 9
his balance is greater.

when x = 10:
her balance is 100 - 8.50 * 10 = 15
his balance is 75 - 6.00 * 10 = 15
their balances are the same.