Question

Explain how the following inequality can be used to find the number of toys you can afford to buy. 150≤ 11x + 10 ≤ 450

Answer 1

The maximum number of toys you can afford to buy is 40

Explanation:

Let

x -----> the number of toys

we have the compound inequality

`150\leq 11x+10\leq 450`

Divide into two inequalities

`150\leq 11x+10` -----> inequality A

`11x+10\leq 450` ----> inequality B

Solve the inequality A

`150-10\leq 11x`

`140\leq 11x`

Divide by 11 both sides

`12.7\leq x`

Rewrite

`x\geq 12.7`

Solve the inequality B

`11x\leq 450-10`

`11x\leq 440`

Divide by 11 both sides

`x\leq 40`

The solution for x is the interval ----> [13,40}

Remember that the number of toys must be a whole number

The domain is all whole numbers greater than or equal to 13 toys and less than or equal to 40 toys

therefore

The maximum number of toys you can afford to buy is 40