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Need Help! The cost of three notebooks and four pencils is $7.20. The cost of five notebooks and eight pencils is $13.20. Write a system of equations to model this situation. How much does one pencil and one notebook cost?

would also like steps, but that optinal

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Dragonforce

Answer:

3n+4p=7.20

5n+8p=13.20

p=.9

n=1.20

Step-by-step explanation:

n is for notebooks, p is for pencils

3n+4p=7.20

5n+8p=13.20

Let's solve for n

 -2(3n+4p=7.20)

so

-6n-8p=-14.40

+ 5n+8p=13.20

-1n=-1.20

divide by -1 to get the fraction by itself

n=1.20

plug in n for one of the equations to solve for p

5(1.20)+8p=13.20

6+8p=13.20

subtract 6 from both sides

8p=7.2

divide by 8 to get p by itself

p=.9

plug n and p in both equations to see if it adds up to the correct answer

5(1.2)+8(.9)=13.2

6 + 7.2 =13.2

13.2=13.2 which is equal so it's correct

Answer: 3n +4p = 7.20

5n+8p=13.20

pencil = $0.9

Notebook =$1.2

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

  • cost of three notebooks and four pencils: $7.20

The equation for this statement is:

3n +4p = 7.20 (a)

where:

n = cost of one notebook

p = cost of one pencil

  • cost of five notebooks and eight pencils : $13.20

5n+8p=13.20(b)

So, isolating n in (a)

3n +4p = 7.20

3n  = 7.20 -4p

n = (7.20 -4p)/3

n = 2.4 - 4/3 p

Replacing "n" in (b)

5n+8p=13.20

5 (2.4 - 4/3 p)+8p =13.20

12-20/3p +8p =13.20

-20/3 p +8p =13.20-12

4/3 p = 1.2

p = 1.2 / (4/3)

p= 0.9

Replacing "p" in(a)

3n +4p = 7.20

3n +4(0.9) = 7.20

3n +3.6 =7.20

3n =7.20-3.6

3n =3.6

n =3.6/3

n= 1.2

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