32.4k views
0 votes
Gabriel is buying pens and notebooks for school. Pens cost $1.50 each, and notebooks cost $3.00 each. She buys a total of 15 items and spends $30. How many pens and notebooks did Gabriel buy?

User Lindlof
by
7.9k points

1 Answer

3 votes

To find the number of pens and notebooks Gabriel bought, let's use a system of equations.

Let's assume Gabriel bought x pens and y notebooks.

According to the problem, pens cost $1.50 each and notebooks cost $3.00 each. Therefore, the total cost can be calculated as follows:

Total cost = (Cost of pens * Number of pens) + (Cost of notebooks * Number of notebooks)

30 = (1.50 * x) + (3.00 * y)

The problem also states that Gabriel bought a total of 15 items. So, the total number of items can be expressed as:

Total items = Number of pens + Number of notebooks

15 = x + y

We now have a system of equations:

1.50x + 3.00y = 30

x + y = 15

To solve this system of equations, we can use substitution or elimination. Let's use the elimination method.

Multiply the second equation by 1.50 to make the coefficients of x in both equations the same:

1.50(x + y) = 1.50(15)

1.50x + 1.50y = 22.50

Now, subtract the first equation from the modified second equation:

(1.50x + 1.50y) - (1.50x + 3.00y) = 22.50 - 30

-1.50y = -7.50

y = -7.50 / -1.50

y = 5

Substitute the value of y into the second equation:

x + 5 = 15

x = 15 - 5

x = 10

Therefore, Gabriel bought 10 pens and 5 notebooks.

User Eric Czech
by
8.3k points