Question

lyla buys 30 balloons. she buys foil balloons for $5.49 each and toy balloons for $2.29 each. she pays a total of $123.10 for the balloons. write a system of linear equations, and find the number of foil balloons f and the number of toy balloons t she buys. let x = # of foil balloons let y = # of balloons

Explanation:

Step1: Set up the quantity - related equation

The total number of balloons is 30. If $x$ is the number of foil balloons and $y$ is the number of toy balloons, then $x + y=30$, which can be rewritten as $y = 30 - x$.

Step2: Set up the cost - related equation

Foil balloons cost $5.49$ each and toy balloons cost $2.29$ each, and the total cost is $123.10$. So, $5.49x+2.29y = 123.10$.

Step3: Substitute $y$ into the cost equation

Substitute $y = 30 - x$ into $5.49x+2.29y = 123.10$:
\[

$$\begin{align*} 5.49x+2.29(30 - x)&=123.10\\ 5.49x+68.7-2.29x&=123.10\\ (5.49x - 2.29x)+68.7&=123.10\\ 3.2x+68.7&=123.10\\ 3.2x&=123.10 - 68.7\\ 3.2x&=54.4\\ x&=\frac{54.4}{3.2}\\ x& = 17 \end{align*}$$

\]

Step4: Find the value of $y$

Substitute $x = 17$ into $y = 30 - x$, we get $y=30 - 17=13$.

Answer:

The number of foil balloons $x = 17$ and the number of toy balloons $y = 13$.