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Holly earned $ 390 in the school bake sale. She sold a total of 40 pastries between cakes and dozens of donuts. One cake was sold for $ 15 and one dozen of donuts was worth $ 8. Let c represent the number of cakes, and let d represent the number of dozens of donuts.

User Yen
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1 Answer

3 votes

Answer:

c = 10; d = 30

Explanation:

As one commenter implies, we will need a system of equations to solve for c, the number of cakes sold, and d, the number of dozens sold.

We know that the sum of the revenues (price * quantity) earned from the cakes and doughnuts equals the total revenue:

(price of cake * quantity of cake) + (price of dozen + quantity of dozen) = total revenue.

First equation: Since the price of one cake is $15, the price of one dozen of doughnuts is $8, and the total revenue earned is $390, our first equation is:

15c + 8d = 390

We further know the sum of the total number of cakes and dozens sold equals the total amount of pastries sold:

total number of cakes + total number of dozens = total amount of pastries.

Second equation: Since the total amount of pastries sold is 40, our second equation is:

c + d = 40

Method to solve for c and d: Substitution

Step 1: Isolate c in the second equation to prepare for substitution:

(c + d = 40) - d

c = -d + 40

Step 2: Substitute -d + 40 for c in 15c + 8d = 390 (first equation in system) to solve for d:

15(-d + 40) + 8d = 390

-15d + 600 + 8d = 390

-7d + 600 = 390

-7d = -210

d = 30

Step 3: Plug in 30 for d in c + d = 40 to solve for c:

c + 30 = 40

c = 10

Thus, the number of dozens sold was 30 and the number of cakes sold was 10.

Optional Step 4: Check validity of answers by plugging in 30 for d and c for 10 in both c + d = 40 and 15d + 8c = 390:

Plugging in 30 for d and 10 for c in c + d = 40:

10 + 30 = 40

40 = 40

Plugging in 30 for d and 10 for c in 15d + 8c = 390:

15(10) + 8(30) = 390

150 + 240 = 390

390 = 390

Thus, our answers are correct

User Teck
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