Question

Katie bought 9 writing utensils for a total of $22.00. Pens cost $3.00 and pencils cost $2.00. How many pencils did she buy?

Answer 1

Katie bought 5 pencils after setting up a system of equations: x + y = 9 and 2x + 3y = 22. After solving the system, we find y = 4 pens, and thus x = 5, the number of pencils.

Step-by-step explanation:

Let’s define variables to solve the problem: Let x be the number of pencils Katie bought, and let y be the number of pens. Since Katie bought 9 writing utensils in total, we have the equation:

x + y = 9

The total cost of the writing utensils is $22. Pencils cost $2.00 each and pens cost $3.00 each, which gives us the second equation:

2x + 3y = 22

Using these two equations, we can solve for x and y. First, we can multiply the first equation by 2 to help eliminate one variable:

2(x + y) = 2(9) ⇒ 2x + 2y = 18

Now we will subtract this new equation from the second equation:

(2x + 3y) - (2x + 2y) = 22 - 18

This simplifies to:

y = 4

Using this value of y in the first equation, we substitute 4 for y:

x + 4 = 9

So, we find:

x = 5

Therefore, Katie bought 5 pencils.