Question

5. At the annual fall festival, Laney sets up a booth and sells wreaths and flower bouquets She has already received some requests,

so she knows she will need to make at least 8 houquets. Due to a shortage of evergreen branches, she cannot make more than
10 wreaths. In the month leading up to the festival, Laney will have time to put together at most 25 arrangements (either wreaths
or bouquets).
a. Write a system of inequalities for the scenario describing b bouquets and u wreaths

Answer 1

The system of inequalities for Laney's wreaths and bouquets is: b ≥ 8 (at least 8 bouquets), w ≤ 10 (no more than 10 wreaths), and b + w ≤ 25 (at most 25 arrangements total).

Step-by-step explanation:

The student is asked to write a system of inequalities based on the given scenario involving Laney setting up a booth to sell wreaths and flower bouquets at the annual fall festival. Let's define 'b' as the number of bouquets and 'w' as the number of wreaths that Laney will make. Here are the inequalities based on the constraints provided:

Laney knows she needs to make at least 8 bouquets: b ≥ 8

Due to a shortage of evergreen branches, she can't make more than 10 wreaths: w ≤ 10

Laney has time to put together at most 25 arrangements, which can be either wreaths or bouquets: b + w ≤ 25

These inequalities form the system that describes the possible combinations of bouquets and wreaths Laney can make for the festival.

Answer 2

Step-by-step explanation:

Let x and y stand for the numbers of Wreath and Flower bouquets, respectively.

We are told that:

x + y
`\geq` 8

and that:

x
`\leq` 10

plus:

x + y
`\leq` 25

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We can plot these inequalities to define the combinations of x and y that meet the requirements they set forth. See the attached image.

Any combination of wreath and flower bouquets found within the marked trapezoid are valid combinations of bouquets. The sample point (5,10) means that 5 wreath and 10 flower bouquets is a possible solution that meets all the requirements set forth above.

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Is (5,10) a valid combination?

x + y
`\geq` 8 5+10≥ 8? YES

x
`\leq` 10 5
`\leq` 10? YES

x + y
`\leq` 25 5 + 10
`\leq` 25? YES

Many other combinations are also possible. We need additional information to determine anythng more specific.