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emilysawyer4363
03.03.2021 •
Mathematics
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?
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Ответ:
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 =![\frac{43.5}{29}](/tpl/images/1164/6418/212e4.png)
= 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.
Ответ:
Thank you!
Step-by-step explanation:
Someone needs to say it!