Answer:
Diane purchased 7 pens
Step-by-step explanation:
Let
x----> the number of pens
y----> the number of pencils
we know that
x+y=17
y=17-x -----> equation A
0.60x+0.40y=8.20 -----> equation B
Solve the system of equations by substitution
Substitute equation A in equation B and solve for x
0.60x+0.40(17-x)=8.20
0.60x+6.8-0.40x=8.20
0.20x=8.20 -6.8
x=1.4/0.2=7 pens
Answer: The number of pen purchased by Diane is 7.
Step-by-step explanation: Given that Joe’s department store sells pens for 60 cents each and pencils for 40 cents each.
Diane purchased a total of 17 items for $8.20.
We are to find the number of pen that Diane purchased.
We know that
1 cent = $ 0.01.
Let x and y represents the number of pen and pencils that Diane purchased.
Then, according to the given information, we have
[tex]60\times0.01x+40\times 0.01y=8.20\\\\\Rightarrow 0.6x+0.4y=8.20\\\\\Rightarrow 6x+4y=82~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
and
[tex]x+y=17\\\\\Rightarrow y=17-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Substituting the value of y from equation (ii) in equation (i), we get
[tex]6x+4y=82\\\\\Rightarrow 6x+4(17-x)=82\\\\\Rightarrow 6x+68-4x=82\\\\\Rightarrow 2x=82-68\\\\\Rightarrow 2x=14\\\\\Rightarrow x=\dfrac{14}{2}\\\\\Rightarrow x=7.[/tex]
Thus, the number of pen purchased by Diane is 7.
