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Three pencils and one pen costs $1.20. Seven pencils and two pens cost $2.50. No prices include tax. In cents, what is the cost of a pencil?

2 Answers

4 votes

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.

User HelloSadness
by
8.2k points
4 votes

Answer:

10 cents

Explanation:

Pre-Solving

We know that the total of three pencils and one pen is equal to $1.20, and that the total of seven pencils and two pens is $2.50.

We can solve this by writing a system of equations. We can say that the price of one pencil is x, and the price of one pen is y.

This means that 3x + y = 1.20 and 7x + 2y = 2.50 because the total cost of 3 pencils will be three times the cost of one pencil for instance.

Solving

Here's our system:

3x + y = 1.20

7x + 2y = 2.50

We can solve this by substitution, where we solve the system for one of the variables to get an expression. Then, we use that expression to get the value of the other variable.

To start, subtract 3x from both sides:

3x + y = 1.20

-3x -3x

_____________________

y = 1.20 - 3x

Now, use 1.20 - 3x as y in 7x + 2y = 2.50 to get:

7x + 2(1.20-3x) = 2.50

7x + 2.40 - 6x + 2.50

x + 2.40 = 2.50

x = 0.10

Since the price of a pencil is x, this means that one pencil is $0.10, or 10 cents.

User Semperos
by
8.1k points