Question

Manuel wants to raise between $250and $350 for charity. His parentsdonated $70. Manuel plans to askothers to contribute $10 each. Howmany people will need to contributefor Manuel to reach his goal?a. Write an inequality to solve theproblem.

Answer 1

Let's call C the amount Manuel raises for charity.

Manuel objective is:

`250\text{ }<=\text{ C <= 350}`

Let's say that the money Manuel has to raise to get to his goal is G. Before he raises any money, we have G = C.

Now, his parents donate 70, so G = C - 70. Replacing in the first equation:

`\begin{gathered} 250\text{ <= C <= 350 } \\ 250\text{ <= G + 70 <= 350} \\ 250\text{ - 70 <= G <= 350 - 70 (substract 70)} \\ 180\text{ <= G <= 280} \end{gathered}`

And Manuel has to raise between 180 and 280 to get to his goal.

Since he plans to ask for 10 to every person he ask to contribute:

`\begin{gathered} (180)/(10)\text{ = 18} \\ \text{and} \\ (280)/(10)\text{ = 28} \end{gathered}`

Manuel has to make between 18 and 28 persons to contribute.

If P is the number of persons, and since they are all giving 10, we can write that as:

`180\text{ <= 10}\cdot P\text{ <= 280}`

If we want to take into account Manuel parents, we can write it as:

`250\text{ <= 10}\cdot P\text{ + 70 <= 350}`

This is point a answer.