Question

Solve each problem by writing an equation that matches the situationthen solve your equation to find the solution.

Answer 1

Question 2:

- Shakira paid $3 to rent shoes for bowling. At this point, she has spent a total of $3.

- Next, she plays bowling games each worth $4.75. This means that:

For her 1st game, she will pay $4.75

For her 2nd game, she will pay 2($4.75)

For her 3rd game, she will pay 3($4.75)

For her 4th game, she will pay 4($4.75)

And so on.

- We can see that her total cost paying for the games follows a pattern and we can therefore generalize. If Shakira plays n games, it means that:

For her nth game, she will pay n($4.75).

- Thus, the total amount that Shakira pays is the amount paid for the shoes plus the amount paid for the games.

- Thus, we can write the equation showing her total cost as follows:

`\begin{gathered} \text{Total cost}=Amt\text{ paid for the shoes }+Amt\text{ paid for the games} \\ \text{Amt paid for the shoes}=3 \\ \text{Amt paid for the shoes}=4.75n \\ \\ \therefore\text{Total Cost}=4.75n+3 \\ \text{where, n is the number of games} \end{gathered}`

- Since Shakira spent a total of $42, we can find the number of games (n) that she played as follows:

`\begin{gathered} 42=4.75n+3 \\ \text{Subtract 3 from both sides} \\ 42-3=4.75n \\ 4.75n=39 \\ \text{Divide both sides by 4.75} \\ (4.75n)/(4.75)=(39)/(4.75) \\ \\ \therefore n=8.21 \\ \text{ Since she cannot pay a decimal number of games, we should round the number down} \\ \\ \therefore n=8 \end{gathered}`

Question 3:

- In solving this question, we shall convert the information given to a mathematical equation

- Let the number of Field trips taken last year be f.

- Three times as many field trips as last year implies

`3f`

- Two more than three times as many field trips as last year implies

`2+3f`

- Cornell's class takes Two more than three times as many field trips as last year and this number of trips this year is 8.

Thus, we can say:

`2+3f=8`

- This means we can find the number of field trips last year f by solving the above expression.

`\begin{gathered} 2+3f=8 \\ \text{Subtract 2 from both sides} \\ 3f=8-2 \\ 3f=6 \\ \text{Divide both sides by 3} \\ (3f)/(3)=(6)/(3) \\ \\ \therefore f=2 \end{gathered}`

Final Answer

Question 2:

- The number of games is 8

- The equation is:

`42=4.75n+3`

Question 3:

- The number of field trips from last year is 2

- The equation is:

`2+3f=8`