Tina can spend up to $60 on DVDs and CDs. She buys used DVDs that cost $9.50 each.  The CDs she buys at a discount for  $12 each. Write an inequality to model the situation. Then, determine the...

Tina can spend up to $60 on DVDs and CDs. She buys used DVDs that cost $9.50 each.  The CDs she buys at a discount for  $12 each. Write an inequality to model the situation. Then, determine the constraints on the variables.

Asked on by taylorruth

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embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

Tina buys DVDs for $9.50 and CDs for $12. She can spend at most $60.

Let x represent the number of DVDs, and y the number of CDs.

Then the amount spent on DVDs is 9.5x, and the amount spent on CDs is 12y. The total amount spent is the sum 9.5x+12y. Since the total amount spent is less than or equal to $60, we have:

`9.5x+12y<=60 `

Since 60 divided by 9.5 is approximately 6.31, Tina can buy at most 6 DVDs. Since 60 divided by 12 is 5, Tina can buy at most 5 CDs. Native integote that Tina cannot buy a negative number of items, and the domain of the variables is the nonnegative integers.

The constraints on the variables are:

`0<=x<=6,0<=y<=5 ` and `9.5x+12y<=60 `

` `

rachellopez's profile pic

rachellopez | Student, Grade 12 | (Level 1) Valedictorian

Posted on

You will need two variables, one for DVD's (x) and one for CD's (y). You know that each DVD is $9.50 and each CD is $12. If you don't want to go over $60 your inequality would be `9.50x + 12y <= 60`. I'm not positive about how to do constraint variables (I've never really learned about them), so I can't confidently tell you exactly how it's written. However, like embizze said, if you divide 60 by each price, that should tell you how many DVD's and CD's you could get max, and any amount under 0 would be impossible.

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