Tyler bought 3 calculators and 7 pens for $67.80. Barbara bought 6 calculators and 2 pens for $92.40. How much does each pen cost?

I think the answer is 3.45$ for each pen

Each pen costs $3.6

Step-by-step explanation:

Solving Simultaneous equations by substitution method.

Step 1

Let us assume a calculator costs $C

Then, 3 calculators costs 3 X $C = $3C

And, 6 calculators costs 6 X $C = $6C

Also, let us assume a pen costs $P

Then, 7 pens cost 7 X $P = $7P

And 2 pens cost 2 X $P = $2P

Step 2

Tyler bought 3 calculators and 7 pens for 67.80

3C + 7P = 67.80

Barbara bought 6 calculators and 2 pens for 92.40

6C + 2P = 92.40

Step 3

The sentence gives us two equations that are simultaneous. We label the first equation as (1) and the second equation, equation (2)

3C + 7P = 67.80 ... (1)

6C + 2P = 92.40 ... (2)

Step 4

Solve the simultaneous equations by substitution method.

In equation (1), we make C the subject

3C + 7P = 67.80 ... (1)

C = (67.80 - 7P) / 3

C = 22.60 - 7P/3 ... (3)

Step 4

Substitute equation (3) into equation (2)

6C + 2P = 92.40 ... (2)

6 (22.60 - 7P/3) + 2P = 92.40

135.60 - 42P/3 + 2P = 92.40

Multiply through by 3

406.80 - 42P + 6P = 277.2

406.80 - 36P = 277.2

Collect like terms

406.80 - 36P - 406.80 = 277.2 - 406.80

-36P = - 129.6

Divide both sides of the equation by - 36

-36P/-36 = - 129.6/-36

P = 3.6

Since P = cost of 1 pen, the cost of one pen is $3.6