Question

Tina bought some nail polish and lip gloss at the store. The nail polish cost $4.50 per bottle and lipgloss cost $7 per tube. Tina bought 9 items and spent $50.50 how many of each item did she buy?

Answer 1

She brought 4 lip gloss and 5 nail polishes

Answer 2

5 bottle of nail polish and 4 lip gloss.

Explanation:

Let x be the number of bottle of nail polish and y be the number of lip gloss,

∵ Total items are 9,

⇒ x + y = 9

⇒ x = 9 - y -----(1),

Also, total spending is $ 50.50 in which the nail polish costs $4.50 per bottle and lip gloss costs $7 per tube,

⇒ 4.5x + 7y = 50.5

From equation (1),

4.5x + 7(9-x) = 50.5

4.5x + 63 - 7x = 50.5

-2.5x + 63 = 50.5

-2.5x = -12.5

⇒ x =
`(-12.5)/(-2.5)` = 5

Again from equation (1),

5 = 9 - y

⇒ 5 + y = 9

⇒ y = 9 - 5 = 4

Hence, she bought 5 bottle of nail polish and 4 lip gloss.