Pergunta

Write a system of equations to describe the situation below.solve using any method, and fill in the blanks. Pete likes to make desserts for bake sales . Last month, he made 1 batch of brownies and 3 batches of cookies, which called for 15 eggs total. The month before, he baked 2 batches of brownies and 3 batches of cookies, which required a total of 18 eggs. How many eggs did Pete use for a batch of each dessert? Pete uses square eggs to make a batch of brownies and square eggs to make a batch of cookies.
Solução

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SuelenEspecialista · Tutor por 3 anos
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Let's denote the number of eggs needed for a batch of brownies as b and the number of eggs needed for a batch of cookies as c. We can set up the following system of equations based on the information provided:
1. b + 3c = 15 (from the first month's data)
2. 2b + 3c = 18 (from the previous month's data)
We can solve this system of equations using the substitution or elimination method. Let's use the elimination method:
First, we can multiply the first equation by 2 to make the coefficients of b in both equations the same:
2b + 6c = 30
Now we have the system of equations:
2b + 6c = 30
2b + 3c = 18
Next, we can subtract the second equation from the first equation to eliminate b:
(2b + 6c) - (2b + 3c) = 30 - 18
3c = 12
Dividing both sides by 3, we get:
c = 4
Now that we have the value of c, we can substitute it back into one of the original equations to solve for b. Let's use the first equation:
b + 3(4) = 15
b + 12 = 15
Subtracting 12 from both sides, we get:
b = 3
Therefore, Pete uses \boxed{3} eggs to make a batch of brownies and \boxed{4} eggs to make a batch of cookies.
1. b + 3c = 15 (from the first month's data)
2. 2b + 3c = 18 (from the previous month's data)
We can solve this system of equations using the substitution or elimination method. Let's use the elimination method:
First, we can multiply the first equation by 2 to make the coefficients of b in both equations the same:
2b + 6c = 30
Now we have the system of equations:
2b + 6c = 30
2b + 3c = 18
Next, we can subtract the second equation from the first equation to eliminate b:
(2b + 6c) - (2b + 3c) = 30 - 18
3c = 12
Dividing both sides by 3, we get:
c = 4
Now that we have the value of c, we can substitute it back into one of the original equations to solve for b. Let's use the first equation:
b + 3(4) = 15
b + 12 = 15
Subtracting 12 from both sides, we get:
b = 3
Therefore, Pete uses \boxed{3} eggs to make a batch of brownies and \boxed{4} eggs to make a batch of cookies.
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