Solve the inequality

Question

Alex pays $8 admission to the county fair and spends $8 on lunch. He buys some ride tickets for $2 each. How many tickets can Alex buy without spending more than $30 at the fair? The inequality 2t + 16 ≤ 30 models this situation, where t is the number of tickets Alex can buy. Solve the inequality. How many tickets can Alex buy?

Answer 1

30 = 2(8) + 2x

2x =30-16 = 14

x=14/2=7 tickets

You can do the inequality, which might be necessary had the solution to the equality been a fraction.

2t +16 is less than or equal to 30

2t is less than or equal to 14

t is less than or equal to 7

But since 7 is an integer, that's the answer, 7.

Answer 2

2t + 16 ≤ 30 Subtract 16 from both sides of the equation

2t + 16 -16 ≤ 30 - 16 Simplify

2t ≤ 14 Divide both sides by 2

2t/2 ≤ 14/2 Simplify

t ≤ 7

He can buy 7 ride tickets and not be over his $30 budget.

Answer 3

Question: HOW MANY TICKETS CAN ALEX BUY?

Let T = the maximum number of tickets Alex can purchase

2T = the amount spent on tickets

8 + 8 + 2T <= 30

16 + 2T <= 30 (Adding 8 + 8)

16 - 16 + 2T <= 30 - 16 (Subtracting 16 from both sides of the equation.)

2T <= 14 (16's cancel each other out and 30 - 16 = 14.)

2T/2 <= 14/2 (Dividing both sides by 2.)

T <= 7 (2's cancel each other out and 14/2 = 7.)

ANSWER: ALEX CAN PURCHASE A MAXIMUM OF 7 TICKETS

CHECKING: $8 + $8 + (7) ($2) = $16 + $14 = $30

If he purchased 8 or more tickets, he would be over his $30 limit.

Hope this was helpful MILES C.