Question

Write and solve the inequality. Let x represent the number of pairs of earrings Julia can purchase.

a. 24x + 8 5 80

c. x + 24 = 80

XS3

x = 56

b. 8x + 24 < 80;

d. 8x + 24 > 80;

x 57

x7

Answer 1

x= 7 pairs,
`24+8x\leq 80`

Explanation:

Here is the complete question: Julia has $80. She want to purchase a nail paint set for $24 and earrings. She spends the rest of the money on earrings. Each pair of earring cost $8. What is the maximum number of earring she can purchase? Write and solve the inequality. Let x represent the number of pairs of earrings Julia can purchase.

Given: Total amount= $80

Cost of nail paint= $24

Each pair of earring cost= $8

Number of pair of earring is "x".

As we know Julia want a nail paint and earrings, also we know x is the number of earring, which Julia can purchase.

Total cost=
`(cost\ of\ each\ nail\ paint)* quantity + (cost\ of\ each\ earring\ pair)* quantity`

We can use the formula and values to form an inequality.

∴
`(\$24* 1)+ (\$8 * x)\leq \$ 80`

⇒
`24+8x\leq 80` (∵ Maximum Julia can spend is $80)

Inequality is
`24+8x\leq 80`

Now, finding number of pair of earring purchased.

Solving
`24+8x\leq 80`

subtracting 24 on both side

`8x\leq 56`

Cross multiplying both side.

∴
`x= (56)/(8) = 7\ pairs\ of\ earring`

∴ Julia can purchase 7 pairs of earring.