Mathematics: Ashley goes to the fair. She is charged $15.00 for admission plus $0.50 for each ride ticket. Ashley has $24.00 to spend at the fair. Write and solve an inequality to represent this situation. Explain what the solution to the inequality means in this situation.

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Ashley goes to the fair. She is charged $15.00

nicolerabbit

01.07.2021

Step-by-step explanation:

t is the number of ride tickets she can buy.

$15 + t \times 0.5 \leqslant 24$

she has to pay $15 just for entering. the rest of the money she can use for ride tickets.

so, whatever she does, she has to stay inside the $24 limit, as she does not have more money.

the $15 admission goes off the $24 available money. that leaves $9.

each ride ticket costs $0.50, so she can buy max. 9/0.5 = 18 tickets. she can buy fewer tickets, but she cannot buy more than these 18 tickets.

so, again

$15 + t \times 0.5 \leqslant 24$

$t \times 0.5 \leqslant 24 - 15 = 9$

$t \times 0.5 \leqslant 9$

$t \leqslant 9 \div 0.5 = 9 \div (1 \div 2) = 2 \times 9 \div 1 \\ = 18$

$t \leqslant 18$

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