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evablogger [386]
3 years ago
13

A corner store sells two kinds of baked goods: cakes and pies. A cake costs $5 and a pie costs $7. In one day, the store sold 15

baked goods for a total of $91. How many cakes did they sell?
-I know the answer is 7, but how do you solve it? What's the work?
Thanks.
Mathematics
1 answer:
frutty [35]3 years ago
6 0

Answer:

7 cakes and 8 pies

Step-by-step explanation:

To solve, write two equations: one for the total number and the other for the total sales.

Let c be the number of cakes.

Let p be the number of pies.

So c + p =15, the total sold.

And 5c + 7p = 91 for the total $ sales.

Solve by substitute one equation into another.

c + p = 15 becomes c = 15 - p. Substitute it into 5c + 7p = 91.

5(15-p) + 7p = 91

75 - 5p + 7p = 91

75 + 2p = 91

2p = 16

p=8

To find c, substitute p=8 into c = 15 - p.

c = 15 - 8

c = 7

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Scores on the test are normally distributed with a mean of 79 and a standard deviation of 8.4. Find the numerical limits for a B
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This is not the question, the correct question is:

A humanities professor assigns letter grades on a test according to the following scheme. A: Top 6% of scores B: Scores below the top 6% and above the bottom 59% C: Scores below the top 41% and above the bottom 17% D: Scores below the top 83% and above the bottom 7% F: Bottom 7% of scores.

Scores on the test are normally distributed with a mean of 79 and a standard deviation of 8.4. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.

Answer:  The numerical limits for grade B is 81 and 92

Step-by-step explanation:

Given that

mean Ж = 79

Standard deviation S = 8.4

B: Scores below the top 6% and above the bottom 59%

To find the numerical value for Grade B

Below the top bottom 6% ( 0.06) is

p ( X < Ж ) = 1 - 0.06

p ( X < Ж ) = 0.94

therefore

P( (X - ц)/S < (X - Ж) / S)) = 0.94

(X - 79) / 8.4 = 1.5548 ( from normal distribution table )

X - 79 = 13.0603

X = 13.0603 + 79

X = 92.06 ≈ 92 ( nearest whole number)

Above bottom 59% ( 0.59) is

p ( X < Ж ) = 0.59

therefore

P( (X - ц)/S < (X - Ж) / S)) = 0.59

(X - 79) / 8.4 = 0.2275 ( from normal distribution table )

X - 79 = 1.9114

X = 1.9114 + 79

X = 80.91 ≈ 81 ( nearest whole number)

So the numerical limits for grade B is 81 and 92

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