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:
[tex]\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}[/tex]- Since Shakira spent a total of $42, we can find the number of games (n) that she played as follows:
[tex]\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} \\ \frac{4.75n}{4.75}=\frac{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}[/tex]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
[tex]3f[/tex]- Two more than three times as many field trips as last year implies
[tex]2+3f[/tex]- 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:
[tex]2+3f=8[/tex]- This means we can find the number of field trips last year f by solving the above expression.
[tex]\begin{gathered} 2+3f=8 \\ \text{Subtract 2 from both sides} \\ 3f=8-2 \\ 3f=6 \\ \text{Divide both sides by 3} \\ \frac{3f}{3}=\frac{6}{3} \\ \\ \therefore f=2 \end{gathered}[/tex]Final Answer
Question 2:
- The number of games is 8
- The equation is:
[tex]42=4.75n+3[/tex]
Question 3:
- The number of field trips from last year is 2
- The equation is:
[tex]2+3f=8[/tex]
