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Answer :
For the system of equation yesterday, the bakery sold 16 decorated sugar cookies and 24 miniature cakes.
The total sales were $96, with decorated sugar cookies priced at $3 each and miniature cakes at $2 each.
To solve this system of equations,
use either the substitution method or the elimination method. Let's use the elimination method:
The system of equations:
s + c = 40
3s + 2c = 96
Multiply equation 1 by 2 to make the coefficients of "c" in both equations the same:
2(s + c) = 2 ( 40)
2s + 2c = 80
Subtract the modified equation 1 from equation 2 to eliminate "c":
(3s + 2c) - (2s + 2c) = 96 - 80
3s - 2s = 16
s = 16
Substitute the value of s (which is 16) into equation 1 to find the value of c:
s + c = 40
16 + c = 40
c = 40 - 16
c = 24
Therefore, the number of decorated sugar cookies (s) sold is 16, and the number of miniature cakes (c) sold is 24 for the system of equation.
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To find the number of decorated sugar cookies and miniature cakes sold by the bakery, we solved the system of linear equations, resulting in 16 decorated sugar cookies and 24 miniature cakes sold.
The question involves solving a system of linear equations to determine the number of decorated sugar cookies ( s) and miniature cakes ( c) sold by a local bakery. To solve this system, we use the substitution or elimination method.
Step-by-step explanation
Start with the given system of equations:
s + c = 40 (Equation 1)
3s + 2c = 96 (Equation 2)
Rewrite Equation 1 to express s in terms of c: s = 40 - c.
Substitute the expression for s from step 2 into Equation 2: 3(40 - c) + 2c = 96.
Simplify and solve for c: 120 - 3c + 2c = 96, which simplifies to c = 24.
Substitute c = 24 back into the expression for s to find the value of s: s = 40 - 24, which simplifies to s = 16.
Therefore, the bakery sold 16 decorated sugar cookies and 24 miniature cakes.
