Answer:
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 = [tex]\frac{43.5}{29}[/tex]
= 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.
