To solve this problem, let's set up a system of equations based on the information provided.

Given Information

1. Lyla buys 30 balloons in total.
2. She buys foil balloons at $5.49 each and toy balloons at $2.29 each.
3. She spends a total of $123.10.

Variables

Let:

• $f$ = the number of foil balloons.
• $t$ = the number of toy balloons.

Step 1: Set Up Equations

From the information given, we can write two equations:

1. The total number of balloons: $f + t = 30$

2. The total cost of the balloons: $5.49f + 2.29t = 123.10$

Step 2: Solve the System of Equations

Substitute $t = 30 - f$ (from the first equation) into the second equation:

$5.49f + 2.29(30 - f) = 123.10$

Expand and simplify:

$5.49f + 68.7 - 2.29f = 123.10$

$(5.49 - 2.29)f = 123.10 - 68.7$

$3.2f = 54.4$

$f = \frac{54.4}{3.2} = 17$

Substitute $f = 17$ back into the first equation to find $t$:

$17 + t = 30$

$t = 30 - 17 = 13$

Solution

Lyla bought:

• 17 foil balloons
• 13 toy balloons

Would you like further details or have any questions about this solution?

Related Questions

1. How would the solution change if each foil balloon cost $6.00 instead?
2. How can we verify if our solution satisfies both equations?
3. What if the total cost was $150.00 instead of $123.10?
4. How could we solve this system of equations using matrix methods?
5. How can we interpret the solution graphically?

Tip

When setting up equations from word problems, label your variables clearly and match each part of the problem to ensure all conditions are met.