Question

question 1-4
the equations (6x + 5y = 300) and (3x + 7y = 285) represent the money collected from selling gift baskets in a school fundraising event. if (x) represents the cost for each snack gift basket and (y) represents the cost for each chocolate gift basket, what is the cost for each snack gift basket?
the cost for a snack gift basket is

Explanation:

Step1: Multiply the second equation by 2

We have the system of equations:
\[

$$\begin{cases} 6x + 5y = 300 \\ 3x + 7y = 285 \end{cases}$$

\]
Multiply the second equation \(3x + 7y = 285\) by 2 to get \(6x+14y = 570\). This step is to make the coefficients of \(x\) in both equations the same so that we can eliminate \(x\) by subtraction.

Step2: Subtract the first equation from the new equation

Subtract the first equation \(6x + 5y = 300\) from \(6x + 14y = 570\):
\[
(6x + 14y)-(6x + 5y)=570 - 300
\]
Simplify the left - hand side: \(6x+14y - 6x - 5y=9y\), and the right - hand side: \(570 - 300 = 270\). So we have \(9y=270\).

Step3: Solve for y

Divide both sides of the equation \(9y = 270\) by 9: \(y=\frac{270}{9}=30\).

Step4: Substitute y into the first equation to solve for x

Substitute \(y = 30\) into the first equation \(6x+5y = 300\):
\[
6x+5\times30=300
\]
Simplify: \(6x + 150=300\). Subtract 150 from both sides: \(6x=300 - 150=150\). Then divide both sides by 6: \(x=\frac{150}{6}=25\).

Answer:

The cost for each snack gift basket is 25.