Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. $\newline$ Nora wanted to stock up on drinks for an upcoming party. First, she spent $\$60$ on $15$ cases of juice and $15$ cases of soda, which is all the store had in stock. A few days later, she returned to the store and purchased an additional $5$ cases of juice and $9$ cases of soda, spending a total of $\$28$ . What is the price of each drink? $\newline$ The price for a case of juice is $\$$ , and the price for a case of soda is $\$$

Full solution

Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Nora wanted to stock up on drinks for an upcoming party. First, she spent

\$60

15

cases of juice and

15

cases of soda, which is all the store had in stock. A few days later, she returned to the store and purchased an additional

5

cases of juice and

9

cases of soda, spending a total of

\$28

. What is the price of each drink?

\newline

The price for a case of juice is

\$

____, and the price for a case of soda is

\$

____

Equation $1$ : Let's denote the price of each case of juice as $j$ and the price of each case of soda as $s$ . Nora spent $\$60$ on $15$ cases of juice and $15$ cases of soda. This gives us the equation $15j + 15s = 60$ .
Equation $2$ : On her second trip, Nora purchased $5$ cases of juice and $9$ cases of soda for a total of $\$28$ . This gives us the equation $5j + 9s = 28$ .
Eliminate Variable: We now have a system of two equations. We need to eliminate one of the variables, $j$ or $s$ . To do this, we can multiply the second equation by $3$ to match the coefficient of $j$ in the first equation. This gives us $15j + 27s = 84$ .
Substitute and Solve: We now subtract the first equation from the new third equation to eliminate $j$ . This gives us $12s = 24$ , or $s = 2$ .
Final Solution: We substitute $s = 2$ into the first equation and solve for $j$ . This gives us $15j + 15(2) = 60$ , which simplifies to $15j + 30 = 60$ . Subtracting $30$ from both sides gives us $15j = 30$ , or $j = 2$ .