Answer:
Cost of a pencil = $0.10
Explanation:
We will need a system of equations to determine the cost of a pencil.
Let x represent the cost of a pencil and y represent the cost of a pen
First equation:
Since three pencils and one pen cost $1.20, we know that:
(pencil quantity * price) + (pen quantity * price) = total cost ($1.20)
Thus, our first equation is given by:
3x + y = 1.20
Second equation:
Since seven pencils and two pens cost $2.50, we know that:
(pencil quantity * price) + (pen quantity * price) = total cost ($2.50)
7x + 2y = 2.50
Method to solve system: Elimination
We can eliminate the ys, allowing us to solve for x with the following steps:
Step 1: Multiply 3x + y = 1.20 by -2:
-2(3x + y = 1.20)
-6x - 2y = -2.40
Step 2: Add -6x - 2y = -2.40 and 7x + 2y = 2.50:
-6x - 2y = -2.40
+
7x + 2y = 2.50
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(-6x + 7x) + (-2y + 2y) + (-2.40 + 2.50)
x = 0.10
Thus, the cost of a single pencil is $0.10
Optional: Check work by determining the cost of a pen:
To determine the cost of a single pen, we can plug in 0.10 for x in any of the two equations in our system. Let's use first equation:
Plugging in 0.10 for x in 3x + y = 1.20:
3(0.10) + y = 1.20
0.30 + y = 1.20
y = 0.90
Now we can check that our answers are correct by plugging in 0.10 for x and 0.90 for y in both equations and checking that we get 1.20 on both sides for the first equation and 2.50 on both sides for the second equation:
Checking solutions in 3x + y = 1.20
3(0.10) + 0.90 = 1.20
0.30 + 0.90 = 1.20
1.20 = 1.20
Checking solutions in 7x + 2y = 2.50
7(0.10) + 2(0.90) = 2.50
0.70 + 1.80 = 2.50
2.50 = 2.50
Thus, our answers are correct.