Jason spent a total of $79.80 on 6 pens and 12 erasers for his friends. A pen costs 5 times as much as an eraser. Find the cost of a pen.
Answer:
Let p = pens and E=erasers...
79.80 = 6p +12E (equation 1)
and the next sentence says a pen costs 5times as much as an eraser.
So we have to multiply the eraser value by 5 to get up to the price of a pen.
So the second equation is p = 5E (equation 2)
I would substitute p=5E into equation 1 and solve for E, then sub that value back into the second equation and solve for p
9.5
Let's assume the cost of an eraser is x dollars.
Since a pen costs 5 times as much as an eraser, the cost of a pen would be 5x dollars.
Jason bought 6 pens and 12 erasers, so the total cost would be:
6 pens * (5x dollars/pencil) = 30x dollars for pens
12 erasers * (x dollars/eraser) = 12x dollars for erasers
The total cost is $79.80, so we can set up the equation:
30x + 12x = 79.80
Combining like terms, we have:
42x = 79.80
Dividing both sides by 42, we find:
x = 79.80 / 42
x = 1.90
Therefore, the cost of a pen is 5x = 5 * 1.90 = $<<5*1.90=9.50>>9.50.
To solve this problem, we can set up equations to represent the given information. Let's denote the cost of a pen as "P" and the cost of an eraser as "E".
We are told that Jason spent a total of $79.80 on 6 pens and 12 erasers. The total cost can be represented as:
6P + 12E = 79.80
We are also told that a pen costs 5 times as much as an eraser:
P = 5E
To solve for the cost of a pen, we can substitute the value of P from the second equation into the first equation:
6(5E) + 12E = 79.80
Simplifying the equation:
30E + 12E = 79.80
42E = 79.80
E = 79.80 / 42
E ≈ 1.90
Now that we have found the cost of an eraser, we can substitute this value back into the second equation to find the cost of a pen:
P = 5E
P = 5(1.90)
P ≈ 9.50
Therefore, the cost of a pen is approximately $9.50.