Zahra spent $20.50 on 10 party favors for her party. They party favor for each kid was either a puzzle book or a magic trick. The boys each received a puzzle book that cost $1.75 each. The girls each received a magic trick that cost $2.25 each. How many boys and how many girls attended the party?
$20.50 on 10 party favors.
6 girls will cost $13.5 (6 x 2.25)
4 boys will cost $7 ( 4 x 1.75)
Total cost = $20.50 therefore 6 girls and 4 boys attended the party
Let the number of boys=b
Let the number of girls=g
b+g=10
1.75b + 2.25g=20.50
Solve the following system:
{b+g = 10
1.75 b+2.25 g = 20.5
In the first equation, look to solve for g:
{b+g = 10
1.75 b+2.25 g = 20.5
Subtract b from both sides:
{g = 10-b
1.75 b+2.25 g = 20.5
Substitute g = 10-b into the second equation:
{g = 10-b
2.25 (10-b)+1.75 b = 20.5
2.25 (10-b)+1.75 b = 1.75 b+(22.5-2.25 b) = 22.5-0.5 b:
{g = 10-b
22.5-0.5 b = 20.5
In the second equation, look to solve for b:
{g = 10-b
22.5-0.5 b = 20.5
22.5-0.5 b = 45/2-b/2 and 20.5 = 41/2:
45/2-b/2 = 41/2
Subtract 45/2 from both sides:
{g = 10-b
-b/2 = -2
Multiply both sides by -2:
{g = 10-b
b = 4
Substitute b = 4 into the first equation:
{g = 6
b = 4
Collect results in alphabetical order:
Answer: | b = 4 g = 6
