Question

4. Angie was given a gift card with a $75 balance. She only uses the gift card to purchase her daily cup of chai tea from her favorite café. A cup of tea is $2.85. The equation y = 75 - 2.85x represents the amount of money remaining on the gift card after x cups of tea. a. Identify and interpret the x- and y-intercepts. Round to the nearest tenth, if necessary. b. Predict how many cups of tea Angie has purchased when the gift card balance is about $35.​

Answer 1

Angie originally has $75 on her card.

She only uses the card for a daily cup of tea of $2.85

Then the equation:

y = $75 - $2.85*x

represents the balance on the card after x cps of tea.

a) The x-intercept is the pair (x, 0), meaning that y = 0, so this is the point at which the balance of the card is zero.

Here we need to solve:

0 = $75 - $2.85*x

$2.85*x = $75

x = $75/$2.85 = 26.3

Here we have a particular case because she can not buy 0.3 of a cup of tea, so the card will never reach a balance of $0.

The y-intercept is the pair (0, y) so we have x = 0, then: y = $75 - $2.85*0 = $75

This is the initial balance of the card.

b) Here we need to solve

y = $35 = $75 - $2.85*x

for x

$35 = $75 - $2.85*x

$35 + $2.85*x = $75

$2.85*x = $75 - $35 = $40

x = $40/$2.85 = 14.03

So after 14 cups of tea, the card's balance will be near $35.