Question

Jason buys 2 highlighters and five pens and pays 16. Eddy buys 4 highlighters and 3 pens and pays 18. Determine the cost of a highlighte and the cost of a pen.

Answer 1

Easier method instead of that long convoluting way of the bot:

2H + 5P = 16
4H + 3P = 18

double the first:
4H + 10P = 32
now subtract the second:
7P = 14
P = 2
sub into 2H + 5P = 16
2H + 10 = 16
H = 3

Cost of pen is $2, and the cost of a highlighter is $3.

Answer 2

Let's use H to represent the cost of a highlighter and P to represent the cost of a pen.

From the first sentence, we know that:

2H + 5P = 16

And from the second sentence, we know:

4H + 3P = 18

We can use these two equations to solve for H and P.

One way to do this is to eliminate one of the variables (either H or P) by multiplying one of the equations by a constant and adding or subtracting the two equations.

Let's multiply the first equation by 3 and the second equation by -5:

6H + 15P = 48 (equation 1 x 3)
-20H - 15P = -90 (equation 2 x -5)

Now we can add the two equations:

-14H = -42

Dividing both sides by -14, we get:

H = 3

So a highlighter costs 3 dollars.

We can substitute this value back into one of the original equations to solve for P. Let's use the first one:

2H + 5P = 16

2(3) + 5P = 16

6 + 5P = 16

Subtracting 6 from both sides:

5P = 10

Dividing both sides by 5:

P = 2

So a pen costs 2 dollars.

Therefore, the cost of a highlighter is 3 dollars and the cost of a pen is 2 dollars.

Answer 3

Yes, that's a faster method! Thank you for suggesting it.