Question

Tabitha earns $8.50 per hour at her summer job. She wants to save money to buy a tablet that costs $289 plus 6% sales tax. Tabitha has already saved $75. write and solve an inequality that shows how many hours Tabitha will need to work to have enough money to buy the tablet.

Answer 1

The Inequality that shows number of hours Tabitha will need to work to have enough money to buy the tablet is
`75+8.5x\geq 306.34`.

Tabitha needs to work at least 28 hours to buy the tablet.

Explanation:

Amount earn per hour = $8.50

Amount already saved = $75

Cost of tablet = $289

Sales tax = 6%

We to write and solve the inequality number of hours Tabitha will need to work to have enough money to buy the tablet.

Solution:

Let the number of hours she need to work be 'x'.

First we will find the total amount required to buy tablet.

Amount of sales tax =
`(6)/(100)*289 = \$17.34`

Now Total cost to buy tablet will be equal to sum of Cost of tablet and Amount of sales tax.

framing in equation form we get;

Total cost to buy tablet =
`289+17.34 = \$306.34`

Now we can say that;

Amount already saved plus Amount earn per hour multiplied by Amount earn per hour should be greater than or equal to Total cost to buy tablet.

framing in equation form we get;

`75+8.5x\geq 306.34`

hence The Inequality that shows number of hours Tabitha will need to work to have enough money to buy the tablet is
`75+8.5x\geq 306.34`.

On solving the above Inequality we get;

First we will subtract both side by 75 we get;

`75+8.5x-75\geq 306.34-75\\\\8.5x\geq 231.34`

Dividing both side by 8.5 we get;

`(8.5x)/(8.5)\geq (231.34)/(8.5)\\\\x\geq 27.21`

Hence Tabitha needs to work at least 28 hours to buy the tablet.