When dealing with a system of linear inequalities and a real world scenario, not all of the possible answers make sense.
Would it make sense for you to pay -$200 into a savings account or for a company to charge -$5 for an item they are selling?
The possible answers to a system of linear inequalities are either viable or non-viable.Work through the following problems to identify the solutions that make sense:Problem 1
Problem 2
Problem 3
Amisi wanted to buy at least 20 shirts and tops for her daughters. Shirts were on sale for $12 each and tops were on sale for $3 each. She could spend no more than $120. Use graphing to help Amisi plan how many shirts and tops she can buy.
Let S equal shirts and T equal tops:
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S + T ≥ 20 12S + 3T ≤ 120 |
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The lines on the graph intersect at S = 6.7 and T = 13.3. Even though this is a solution for this system, it is not a viable solution.
Since Amisi is buying shirts and tops, the solution has to be in whole numbers. Amisi cannot buy seven tenths of a shirt or 3 tenths of a top.
Danyal makes toy A for $4. He also makes toy B for $7. The greatest number of toys he can make is 13. He wants to make at least $65.
Write and graph a system of inequalities to represent this situation.
| Number of Toys: | A + B ≤ 13 | |
| Money Danyal can make: | 4A + 7B ≥ 65 |
Danyal can only sell whole toys, so the only viable solutions are the ones in the overlapping shaded area where the solutions for A and B are both whole numbers. Some possible solutions are:
(0, 10), (1, 9), (2, 9), (3, 8) . . . (6, 6).
Notice that there is no viable solution when A equals 7. If Danyel makes 7 of toy A, he will not make more than $65.
Your friend asked how old Vicki and Yolanda are. You know that Vicki is at least 5 years older than her sister, Yolanda. You also know that Vickie is no more than four times Vicki's age minus twice Yolanda's age is less than 20. Vicki is less than 25 years old. How old are Vicki and Yolanda?
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V > Y + 5 4V - 2Y < 20 |
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The overlapping area shows that Vicki is more than 15 and less than 25 years old.
