The Birthday Party Planning
Sophia is planning a birthday party for her friend. She decides to buy balloons and party hats. Each balloon costs $0.50, and each party hat costs $1.20. Sophia buys a total of 20 items and spends $18.40 in total.
How many balloons and how many party hats did Sophia buy?
The total number of items (balloons + hats) is 20. This can be written as:
ReplyDeleteB+H=20
The total cost is $18.40, with balloons costing $0.50 each and hats costing $1.20 each. This can be written as:
0.50B+1.20H=18.40
B+H=20 (Equation 1)
0.50B+1.20H=18.40 (Equation 2)
We can use either the substitution method or the elimination method. For this problem, either method works, but let's use the elimination method as an example.
you can multiply the first equation by 0.50:
0.50B+0.50H=10 (Modified Equation 1)
Subtract One Equation from the Other:
Now, subtract the modified Equation 1 from Equation 2:
(0.50B+1.20H)−(0.50B+0.50H)=18.40−10
Simplifying this gives:
0.70H=8.40
H= 0.70/8.40 =12
Now, substitute
H=12 into one of the original equations (e.g., Equation 1) to find
B+12=20
B=20−12=8
So, the solution is
meaning Sophia bought 8 balloons and 12 party hats.