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olga_2 [115]
3 years ago
15

Help please I need this ASAP

Mathematics
1 answer:
emmasim [6.3K]3 years ago
7 0

Solve for p. We are given:

2m=\frac{p-q}{r}

To get rid of the fraction on the right, multiply both sides by the denominator, which is r.

r(2m)=r(\frac{p-q}{r})

We then get:

2mr=p-q

We are solving for p, so add q to both sides to isolate p on the right side. We are then left with:

2mr+q=p

You could switch the equation to make it look more traditional. However, both answers are correct.

p=q+2mr


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Solution:

1) Use letters to identify the variables:

Number of trumpets: t
Number of clarinets: c

2) Translate each statement into algebraic (mathematical) language.

2.1) Sold a total of 27 used trumpets and clarinets

=> t + c = 27

2.2) Trumpets cost $149 and clarinets cost $99

Total cost of the trumpets: 149t
Total cost of clarinets: 99c

Total cost = 149t + 99c

2.3) Total sales were $3223

=> 149t + 99c = 3223.

3) State the system of equations:

Equation (1) t + c = 27
Equation (2) 149t + 99c = 3223

4) Solve the system of equations:

4.1) Multiply equation 1 by 149:

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4.2) Subtract the equation (2) from the equation obtained in 4.1

=> 149c - 99c = 4023 - 3223

=> 50c = 800

=> c = 800 / 50 = 16

5) Verify the solution:

From equation (1) t = 27 - 16 = 11

Total cost = 149*11 + 99*16 = 3223

Now you have a verified answer: they sold 16 clarinets
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