Question

Joe’s department store sells pens for 60 cents each and pencils for 40 cents each. Diane purchased a total of 17 items (pens and pencils) for $8.20. How many pens did Diane purchase?

Answer 1

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

`60*0.01x+40* 0.01y=8.20\\\\\Rightarrow 0.6x+0.4y=8.20\\\\\Rightarrow 6x+4y=82~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

and

`x+y=17\\\\\Rightarrow y=17-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

Substituting the value of y from equation (ii) in equation (i), we get

`6x+4y=82\\\\\Rightarrow 6x+4(17-x)=82\\\\\Rightarrow 6x+68-4x=82\\\\\Rightarrow 2x=82-68\\\\\Rightarrow 2x=14\\\\\Rightarrow x=(14)/(2)\\\\\Rightarrow x=7.`

Thus, the number of pen purchased by Diane is 7.

Answer 2

Diane purchased 7 pens

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