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Sheena’s Bakery makes and sells cookies and cakes. It costs the store Php580 to buy the supplies needed to make 20 cookies,
and Php400 for the supplies needed to make a cake.
The store sells the cookies for Php40 each and the cakes for Php620 each.
Last month Sheena's Bakery spent Php9880 on supplies and sold all of the cookies and cakes that were made last month
using those supplies for Php14,720.
How many cookies and cakes did they make?
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From the condition, the price to buy a supply for one cookie is 580/20 = Php29.
Therefore, from the condition, you have these two equations
29x + 400y = 9880 (1) (total money to buy supply)
40x + 620y = 14720 (2) (total revenue after selling)
where x is the unknown number of cookies and y is the unknown number of cakes.
To solve the system, apply the determinant method (= the Cramer's rule).
x = = 120;
y = = 16.
ANSWER. 120 cookies and 16 cakes.
Solved.
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On the determinant method (= the Cramer's rule) for 2 equations in 2 unknowns see the lessons
- Solution of the linear system of two equations in two unknowns using determinant
- What is a matrix?,
- Determinant of a 2x2-matrix,
- HOW TO solve system of linear equations in two unknowns using determinant (Cramer's rule),
- Solving systems of linear equations in two unknowns using the Cramer's rule,
- Solving word problems by the Cramer's rule after reducing to systems of linear equations in two unknowns,
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic
"2x2-Matrices, determinants, Cramer's rule for systems in two unknowns"