The cost of an order of 10 computer disks and 3 packages of paper was $27. The next order was for 30 disks and 5 packages, and the cost was $65. Find the cost of a single disk and a single package of paper.
10d + 3p = 27
30d + 5p = 65
from the first, we see
30d + 9p = 81
so, subtracting, we see that
4p = 16
p=4
so, d=2.50
the professor answer for the disk is $1.50 who's right?
well, I see I was wrong. Could you not check my answer?
To find the cost of a single disk and a single package of paper, let's set up a system of equations based on the given information.
Let's represent the cost of a single disk as "d" (in dollars) and the cost of a single package of paper as "p" (in dollars).
From the first order of 10 computer disks and 3 packages of paper costing $27, we can write the equation:
10d + 3p = 27 (Equation 1)
From the second order of 30 disks and 5 packages costing $65, we can write the equation:
30d + 5p = 65 (Equation 2)
Now we have a system of two equations with two variables. We can solve this system to find the values of "d" and "p".
To eliminate one variable, we can multiply Equation 1 by 10 and Equation 2 by 3 to make the coefficients of "d" the same:
(10d + 3p) * 10 = 27 * 10
(30d + 5p) * 3 = 65 * 3
Simplifying:
100d + 30p = 270 (Equation 3)
90d + 15p = 195 (Equation 4)
Now we can solve this system of equations using either substitution or elimination method. Let's use the elimination method to solve for "d" by eliminating "p".
Multiply Equation 4 by 2:
180d + 30p = 390 (Equation 5)
Now subtract Equation 5 from Equation 3:
(100d + 30p) - (180d + 30p) = 270 - 390
Simplifying:
100d - 180d + 30p - 30p = -120
Combine like terms:
-80d = -120
Divide both sides by -80:
d = -120 / -80
d = 1.5
So, the cost of a single disk is $1.5.
Now, substitute the value of "d" into Equation 1 or Equation 2 to find the cost of a single package of paper. Let's use Equation 1:
10(1.5) + 3p = 27
Simplifying:
15 + 3p = 27
Subtract 15 from both sides:
3p = 27 - 15
3p = 12
Divide both sides by 3:
p = 12 / 3
p = 4
Therefore, the cost of a single package of paper is $4.