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ehidna [41]
3 years ago
12

Jack paid $13.75 to buy slices 3 of pizza and 4 hot dogs at a concession stand. Sarah paid $9.75 to buy 2 slices of pizza and 3

hot dogs from the same stand. What was the price of a slice of pizza?
Mathematics
2 answers:
jasenka [17]3 years ago
8 0
$13.75 = 3p + 4d
<span>$9.75 = 2p + 3d
</span>
Using 2nd equation, divide all factors by 3 to isolate hot dog price and solve in terms of pizza price:

3.25 = 2/3p + d
3.25 - 2/3p = d

Now substitute for d in the other equation:

$13.75 = 3p + 4(3.25 - 2/3p)

Distribute the 4: 

$13.75 = 3p + 13 - 8/3p

Combine factors of p:

$13.75 = 9/3p - 8/3p + 13
$13.75 = 1/3p + 13

Isolate and solve for p:

$13.75 -13 = 1/3p

0.75= 1/3p

0.75 * 3 = p
2.25 = p

The price of pizza was $2.25 per slice.
Dovator [93]3 years ago
5 0
The hotdogs cost $1.75, and the pizza cost $2.25.
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Answer:

\displaystyle \sin(A-B)=\frac{495}{1073}

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\displaystyle \tan(A)=\frac{35}{12}\text{ and } \sin(B)=\frac{20}{29}

Where both A and B are positive acute angles.

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For B, the adjacent is 21, opposite is 20, and the hypotenuse is 29.

We can rewrite sin(A-B) as:

\sin(A-B)=\sin(A)\cos(B)-\cos(A)\sin(B)

Using the above conclusions, this yields: (Note that since A and B are positive acute angles, all resulting ratios will be positive.)

\displaystyle \sin(A-B)=\Big(\frac{35}{37}\Big)\Big(\frac{21}{29}\Big)-\Big(\frac{12}{37}\Big)\Big(\frac{20}{29}\Big)

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\displaystyle \sin(A-B)=\frac{735-240}{1073}=\frac{495}{1073}

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