Question

Jamie is buying 5 concert tickets, and he wants his total coast to be no more than $4 above or below $80. Write an inequality that models the cost x, in dollars, of a ticket?

Answer 1

Number of concert tickets Jamie wants to buy = 5

Constraint on total cost is that it should be not beyond $4 above or below $80

Cost of a ticket = x

⇒ 80-4 < x*5 < 80+4

⇒ 76 < 5x < 84

⇒ $\frac{76}{5}$ < x < $\frac{84}{5}$

⇒ 15.2 < x < 16.8

Hence, the inequality that models cost x is: 15.2 < x < 16.8

Answer 2

|80 - 5x| ≤ 4

• This is about absolute value inequality.

He is buying 5 tickets.

He wants his total cost to be in the range of 80 ± 4.

• If the cost of one ticket is $x, then we have;

5x - 80 ≤  4

5x ≤ 84

x ≤ 16.8

• Also; 80 - 5x ≤ 4

5x ≥ 76

x ≥ 15.2

• From absolute values, since;

5x - 80 ≤  4 and 80 - 5x ≤ 4

we can express this inequality as;

|80 - 5x| ≤ 4

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