Q5 - Algebra 1

Question

The table shows donations to help purchase a new tree for the school. How much money did the students donate in all?

Number of students	Amount of Each donation
20	\(250
15	\)325

Step-by-Step Solution

Answer

The students donated $9875 in all to help purchase a new tree for the school.

Step-1. Apply the concept of the four-step process for problem-solving.

Four step plan is used to solve real-world problems with the help of mathematical tools.

Steps involved in the four step plan:

1. Explore/Understand the problem
2. Devise a plan to solve the problem
3. Carry out the plan(solve)
4. Look back (check and interpret)

Step-2. Explore/Understand the problem.

Donations were given by the students:

Number of Students	Amount of Each donation
20	$250
15	$325

An exact solution is required since the amount donated by the students to the school will be a fixed value.

Step-3. Devise a plan to solve the problem.

Total amount donated can be calculated by adding the total amount donated by 20 students and 15 students.

Step-4. Carry out the plan(solve).

Let the total donated amount by 20 students be $A_1$.

It is given that $250 each is donated by 20 students.

Therefore, 

$$\begin{gathered} A_1=\$250\times 20 \\ =\$5000 \end{gathered}$$

Let the total donated amount by 15 students be $A_2$.

It is given that $325 each is donated by 15 students.

Therefore, 

$$\begin{gathered} A_2=325\times 15 \\ =4875 \end{gathered}$$

Hence, the total amount A donated by all the students:

$$\begin{gathered} A=A_1+A_2 \\ =5000+4875 \\ =9875 \end{gathered}$$

Step-5. Look back (check and interpret).

Since the total amount donated is more than individual amounts donated, the answer is verified.

Thus, the students donated $9875 in all to help purchase a new tree for the school.