Question

Mr. Fiore had to go to Party City to buy balloons for Homecoming. He purchased orange balloonsand white balloons. Orange balloons cost $.50 each and white balloons cost $.40 each. Mr. Fiorespent a total of $102.50 and bought a total of 225 balloons. How many orange balloons and how manywhite balloons did he buy?

Answer 1

You know that:

- Orange balloons cost $0.50 each.

- White balloons cost $0.40 each.

- The total amount of money Mr. Fiore spent was $102.50

- He bought a total of 225 balloons.

Let be "o" the number of orange balloons he bought and "w" the number of white balloons he bought.

Using the data given in the exercise, you can set up the following System of Equations:

`\begin{cases}0.5o+0.4w=102.50 \\ \\ o+w=225\end{cases}`

Notice that the total cost of the balloons he bought can be found by adding the total cost of the orange balloons he bought, represented with:

`0.5o`

And the total cost of the white balloons he bought, represented with:

`0.4w`

Then, you get the first equation shown in the system:

`0.5o+0.4w=102.50`

The total number of balloons is the sum of the number of white balloons and the number of orange balloons he bought. That is the meaning of the second equation:

`o+w=225`

Hence, to solve the System of Equations, you can use the Substitution Method:

1. Take the second equation and solve for "o":

`\begin{gathered} o+w=225 \\ o=225-w \end{gathered}`

2. Substitute this new equation into the first original equation and solve for "w", in order to find its value:

`\begin{gathered} 0.5o+0.4w=102.50 \\ \\ 0.5(225-w)+0.4w=102.50 \end{gathered}`
`\begin{gathered} 0.5(225-w)+0.4w=102.50 \\ \\ 112.5-0.5w+0.4w=102.50 \end{gathered}`
`\begin{gathered} -0.1w=102.50-112.5 \\ \\ w=(-10)/(-0.1) \\ \\ w=100 \end{gathered}`

3. Substitute the value of "w" into the equation found in step 1:

`\begin{gathered} o=225-w \\ o=225-(100) \end{gathered}`

4. Evaluating, you get:

`o=125`

Hence, the answer is: He bought 125 orange balloons and 100 white balloons.