Question

1. owen paid a landscaping company $125 for an initial lawn treatment, then $85 per month thereafter. the function p(t)=125 + 85t represents the total amount of money he will have paid after t months. how many months has owen been receiving lawn services if he has paid a total of $2165?

a. 22
b. 24
c. 26
d. 28

1. perry and jose are selling pies for a school fundraiser. customers can buy apple pies and lemon meringue pies. perry sold 7 apple pies and 14 lemon meringue pies for a total of $168. jose sold 7 apple pies and 1 lemon meringue pie for a total of $64. what is the cost each of one apple pie and one lemon meringue pie?

a. apple $8: lemon $8
b. apple $11: lemon $3
c. apple $6: lemon $3
d. apple $9: lemon $9

1. what is the solution to 4(q + 56.5)=30q - 112?

Explanation:

Step1: Set up equation for Owen's problem

We know that $p(t)=125 + 85t$ and $p(t)=2165$. So we set up the equation $125+85t = 2165$.

Step2: Isolate the term with $t$

Subtract 125 from both sides: $85t=2165 - 125=2040$.

Step3: Solve for $t$

Divide both sides by 85: $t=\frac{2040}{85}=24$.

Step4: Set up system of equations for Perry and Jose's problem

Let $a$ be the cost of an apple - pie and $l$ be the cost of a lemon - meringue pie. We have the system:

$$\begin{cases}7a + 14l=168\\7a+1l = 64\end{cases}$$

Subtract the second equation from the first equation: $(7a + 14l)-(7a + l)=168 - 64$.
$7a+14l - 7a - l=104$, $13l = 104$, so $l = 8$.
Substitute $l = 8$ into $7a + l=64$, we get $7a+8 = 64$, $7a=64 - 8=56$, $a = 8$.

Step5: Solve the equation for $q$

Expand the left - hand side of $4(q + 56.5)=30q-112$: $4q+226=30q - 112$.
Move the terms with $q$ to one side and constants to the other side: $226 + 112=30q-4q$.
$338 = 26q$.
Divide both sides by 26: $q=\frac{338}{26}=13$.

Answer:

1. B. 24
2. A. Apple $8: Lemon $8
3. $q = 13$