Rodrigo and Melissa went to the art supply store to buy drawing materials. Rodrigo bought 10 pencils and 7 felt-tip markers for a total of $19.00. Melissa bought 3 pencils and 5 felt-tip markers
for a total of $10.05. Which of the following systems of equations could be used to determine
the cost of one pencil, P, and one felt-tip marker, m?

10P + 7m = 19 .......... 1

3P + 5m = 10.05 .......... 2

Step-by-step explanation:

Let the cost of pencil be represented by P, and felt-tip by m. So that;

Rodrigo bought 10 pencils and 7 felt-tip at the cost of $19.0.

⇒ 10P + 7m = 19 .......... 1

Melissa bought 3 pencils and 5 felt-tip at the cost of $10.05.

⇒ 3P + 5m = 10.05 .......... 2

From equations 1 and 2,

10P + 7m = 19 .......... 1

3P + 5m = 10.05 .......... 2

Multiply equation 1 by 3, and 2 by 10 to have;

30P + 21m = 57 ......... 3

30P + 50m = 100.5 ....... 4

Subtract equation 3 from 4,

30P - 30P + 50m - 21m = 100.5 - 57

29m =43.5

m =

 = 1.5

m = 1.5

Substitute the value of m in equation 2,

3P + 5m = 10.05 .......... 2

3P + 5(1.5) = 10.05

3P = 7.5 = 10.05

3P = 3

P = 1.0

Thus, the cost of a pencil is $1.0 and that of a felt-tip is $1.5.

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