Rushton had $90 to spend at a baseball game. She spent 31/45 of her money on her ticket. Then, she spent 3/7 of her remaining money at the concession stand. While walking back to her seat, she saw a new hat on sale for $18. Did Mme Rushton have enough money left to buy the hat? Show all of your work.

Question

Rushton had $90 to spend at a baseball game. She spent 31/45 of her money on her ticket. Then, she spent 3/7 of her remaining money at the concession stand. While walking back to her seat, she saw a new hat on sale for $18. Did Mme Rushton have enough money left to buy the hat? Show all of your work.

Answer 1

You can solve this with proportions.

x/50=31/45
45x=31(90)
45x=2790
x=62
90-62= 28
After spending money on a ticket, Rushton has 28 dollars remaining.

x/28=3/7
7x=84
x=12
28-12=16
After spending money on concessions, Rushton only has 16 dollars left.

No, Rushton cannot but the hat.

Answer 2

after ticket amount left = (14/45) ( 90) = 28

after concession, amount left = (4/7)(28) = 16
not enough for $18 hat

Answer 3

To determine if Ms. Rushton had enough money left to buy the hat, let's break down her expenses step by step.

First, she spent 31/45 of her money on the ticket. To find out how much money she had remaining, we need to subtract this amount from the total money she started with: $90.

Amount spent on the ticket:
31/45 * $90 = $62

Money remaining after buying the ticket:
$90 - $62 = $28

Next, she spent 3/7 of her remaining money at the concession stand. To find out how much money she had remaining after this expense, we need to subtract this amount from the previous amount remaining:

Amount spent at the concession stand:
3/7 * $28 = $12

Money remaining after the concession stand:
$28 - $12 = $16

Now, she saw a hat on sale for $18. Since the price of the hat ($18) is greater than the money she had remaining ($16), she did not have enough money left to buy the hat. Therefore, she couldn't buy the hat.