orWatch a videoWrite a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Valentina has a home-based business making corsages and boutonnieres for school dances. Last year, she sold 39 corsages and 29 boutonnieres, which brought in a total of $1,465. This year, she sold 27 corsages and 29 boutonnieres, for a total of $1,273. How much does each item sell for?
Question
orWatch a videoWrite a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Valentina has a home-based business making corsages and boutonnieres for school dances. Last year, she sold 39 corsages and 29 boutonnieres, which brought in a total of 1,273. How much does each item sell for?
Solution
Let's denote the cost of a corsage as C and the cost of a boutonniere as B.
From the problem, we can form two equations based on the information given:
- For last year: 39C + 29B = $1465
- For this year: 27C + 29B = $1273
To solve this system of equations using elimination, we can subtract the second equation from the first. This will eliminate B:
(39C + 29B) - (27C + 29B) = 1273 12C = $192
Now, solve for C: C = 16
Substitute C = 16) + 29B = 624 + 29B = 1465 - 841 B = 29
So, each corsage sells for 29.
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