Question 1 (Multiple Choice Worth 1 points) $$ \begin{array}{l} ext { (05.03 MC) } \ ext { Harry had } \$ 32 ext {. He spent all the money buying three notebooks for } x ext { dollars each and four packs of index cards for } y ext { dollars each. If Harry had bought five notebooks and five packs o } \ ext { index cards, he would have run short by } \$ 18 ext {. The following system of equations models this scenario: } \ \begin{array}{l}3 x+4 y=32 \ 5 x+5 y=50\end{array} \ ext { Use the system of equations to solve for } x ext { and } y ext {. }\end{array} $$ ?

Question

Question 1 (Multiple Choice Worth 1 points) $$ \begin{array}{l}	ext { (05.03 MC) } \ 	ext { Harry had } \$ 32 	ext {. He spent all the money buying three notebooks for } x 	ext { dollars each and four packs of index cards for } y 	ext { dollars each. If Harry had bought five notebooks and five packs o } \ 	ext { index cards, he would have run short by } \$ 18 	ext {. The following system of equations models this scenario: } \ \begin{array}{l}3 x+4 y=32 \ 5 x+5 y=50\end{array} \ 	ext { Use the system of equations to solve for } x 	ext { and } y 	ext {. }\end{array} $$ ?

UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{cases}
3x + 4y = 32 \
5x + 5y = 50
\end{cases}
$$

1. **Solve the first equation for $$x$$:**

$$
3x = 32 - 4y \
x = \frac{32 - 4y}{3}
$$

2. **Substitute $$x$$ into the second equation:**

$$
5\left(\frac{32 - 4y}{3}\right) + 5y = 50 \
\frac{160 - 20y}{3} + 5y = 50 \
160 - 20y + 15y = 150 \quad (\text{Multiply through by } 3) \
160 - 5y = 150 \
-5y = -10 \
y = 2
$$

3. **Find $$x$$ using $$y = 2$$:**

$$
x = \frac{32 - 4(2)}{3} = \frac{24}{3} = 8
$$

**Answer:** $$x = 8$$ dollars and $$y = 2$$ dollars.
$$x = 8$$ dollars and $$y = 2$$ dollars.

Question 1 (Multiple Choice Worth 1 points)
?

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions

Question 1 (Multiple Choice Worth 1 points) ?