Question

Elijah and his sister went to the movies. They had 34 altogether and spent 9.50 per ticket. Elijah and his sister bought the same snacks. Write and solve an inequality for the amount that each person spent on snacks. Interpret the solution

Answer 1

The Inequality to find the amount of money they spent on snack is
`2(9.5+x)\leq 34`

Maximum amount each person can spent on snack is 7.5.

Explanation:

Given:

Total Money they had = 34

Cost of each ticket = 9.5

Number of persons = 2

Let the cost of snacks bought by each be x.

We need to write inequality and solve for the amount each persons spent on snacks.

Solution:

Now we can say that;

Number of persons multiplied by sum of Cost of each ticket and Cost of each person spent on snack should be less than or equal to Total money they had.

framing in equation form we get;

`2(9.5+x)\leq 34`

Hence the Inequality to find the amount of money they spent on snack is
`2(9.5+x)\leq 34`

On Solving the above Inequality we get;

`2(9.5+x)\leq 34\\\\19+2x\leq 34`

Now By Using Subtracting property of Inequality we will subtract both side by 19 we get;

`19+2x-19\leq 34-19\\\\2x\leq 15`

No By Division Property of Inequality we will divide both side by 2 we get;

`(2x)/(2)\leq (15)/(2)\\\\x\leq 7.5`

Hence maximum amount each person can spent on snack is 7.5.

Interpreting the solution we get;

Now Cost of 1 ticket = $9.5

Number of person = 2

So total cost of ticket = $19

Total money they have = $34

Money left = Total money - total cost of ticket =$34 -$19 = $15

Amount of money left = $15

Now each buys the same snack.

So maximum amount of money each can spent on snack = $7.5