Respuesta :
Diane purchased 7 pens
Explanation:Cost of one pen = 60 cents = 60/100 = $0.60
Cost of one pencil = 40 cents =40/100 = $0.40
let the number of pens bought = x
let the number of pencils bought = y
[tex]\begin{gathered} \text{Diane bought a total of 17 items}\colon \\ nu\text{mber of pens + number of pencils = 17} \\ x\text{ + y = 17 }\ldots equation\text{ 1} \end{gathered}[/tex][tex]\begin{gathered} \text{The cost of the 17 items = \$8.20} \\ nu\text{mber of pens(cost per one) + number of pencils(cost per one) = 8.20} \\ x(0.60)\text{ + y(0.40) = 8.20 } \\ x(0.6)\text{ + y(0.4) = 8.20 } \\ 0.6x\text{ + 0.4y = 8.2 ...equation 2} \end{gathered}[/tex]combining both equatons:
x + y = 17 ....equation 1
0.6x + 0.4y = 8.2 ...equation 2
using substitution method:
let's make x the subject of formula
from equation 1:
x = 17 - y ....equation 3
substitute for x in equation 2:
0.6(17 - y) + 0.4y = 8.2
10.2 - 0.6y + 0.4y = 8.2
collect like terms:
10.2 - 0.2y = 8.2
10.2 - 8.2 = 0.2y
2 = 0.2y
y = 2/0.2
y = 10
substitute for y in equation 1:
x + 10 = 17
x = 17 - 10
x = 7
x = number of pens = 7
Hence, Diane purchased 7 pens
