Asked by Emma
It takes a florist 3 hour and 15 minutes to make 3 small centerpieces and 3 large centerpieces. It takes 6 hours and 20 minutes to make 4 small centerpieces and 7 large centerpieces. How long does it take to make each small centerpiece and each large centerpiece? write and solve a system of equations to find your answers.
Answers
Answered by
Reiny
let the time taken to make large piece be x hrs
let the time taken to make the small piece by y hrs
3x + 3y = 3 1/4 = 13/4 (#1)
7x + 4y = 6 1/3 = 19/3 (#2)
#1 times 4: 12x+12y = 13
#2 times 3: 21x+12y=19
subtract them ...
9x = 6
x = 2/3 hour or 40 minutes
in #1
3(2/3) + 3y = 13/4
2 + 3y = 13/4
3y = 13/4 - 2 = 5/4
y = 5/12 hours or 25 minutes
let the time taken to make the small piece by y hrs
3x + 3y = 3 1/4 = 13/4 (#1)
7x + 4y = 6 1/3 = 19/3 (#2)
#1 times 4: 12x+12y = 13
#2 times 3: 21x+12y=19
subtract them ...
9x = 6
x = 2/3 hour or 40 minutes
in #1
3(2/3) + 3y = 13/4
2 + 3y = 13/4
3y = 13/4 - 2 = 5/4
y = 5/12 hours or 25 minutes
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