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?

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carlosego carlosego · Answer 1 · 2019-03-15T21:13:54+01:00

Answer:

Notebook cost = $1.2

Pencil cost = $ 0.9

Step-by-step explanation:

Call x at the cost of each notebook and call z at the cost of each pencil.

So we know that 3x added with 4z equals $ 7.20

So:

[tex]3x + 4z = \$ 7.20[/tex] (i)

We also know that 5x and 8z = $13.20

Then:

[tex]5x + 8z = \$13.20[/tex] (ii)

Finally we have a system of 2 equations (i), (ii) and two unknowns x and z.

Then we can solve the system by doing:

-2(i) + (ii)

We have left:

[tex]-6x - 8z = \$-14.4[/tex]

+

[tex]5x + 8z = \$13.20[/tex]

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[tex]-x = -1.2\\x = \$1.2[/tex]

Now we substitute the value of x in equation (i) and clear z.

[tex]3(1.2) + 4z = \$7.20\\\\4z = 3.6\\\\z = \$0.9[/tex]