The school store opened on the first day of school with 45 notebooks and 15 pencils. Within two days it sold all of these items. On the first day, twice as many notebooks were sold as pencils. On the second day, for every 7 notebooks sold, 2 pencils were sold. How many notebooks and how many pencils were sold on each day?

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26-03-2020
Mathematics

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The school store opened on the first day of school with 45 notebooks and 15 pencils. Within two days it sold all of these items. On the first day, twice as many notebooks were sold as pencils. On the second day, for every 7 notebooks sold, 2 pencils were sold. How many notebooks and how many pencils were sold on each day?

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bhuvna789456 bhuvna789456 · Answer 1 · 2020-04-04T09:14:27+02:00

The number of pencils sold on the first day is 5 pencils.

The number of notebooks sold on the first day is 10 notebooks.

The number of pencils sold on the second day 10 pencils.

The number of notebooks sold on the second day 35 notebooks.

Step-by-step explanation:

Given data,

The total number of notebooks in the store = 45 notebooks.
The total number of Pencils in the store = 15 pencils.
The number of days that all items were sold = 2 days.

Now, you have to calculate the no.of notebooks and no. of pencils sold each day.

In the first day :

The number of sale of notebooks and pencils are given by,

Twice as many notebooks were sold as pencils.

Let us take, the number of pencils sold on the first day = x

And, the number of notebooks sold on the first day = 2x (Twice as pencils).

In the second day :

The number of sale of notebooks and pencils are given by,

For every 7 notebooks sold, 2 pencils were sold.

The number of pencils sold on the second day = 2y

The number of notebooks sold on the second day = 7y

The equation is framed for number of notebooks sold on each day :

The number of notebooks sold ⇒ 2x + 7y = 45 -------(1)

The equation is framed for number of pencils sold on each day :

The number of pencils sold: x + 2y = 15 ----------(2)

Solving the equations by multiplying eq(2) by 2 and subtract it from eq(1),

2x + 7y = 45

- (2x + 4y) = 30

3y = 15

⇒ y = 15/3

⇒ y = 5

The value of y is 5.

Substitute y=5 in eq (2),

⇒ x + 2(5) = 15

⇒ x + 10 = 15

⇒ x = 15 - 10

⇒ x = 5

The value of x is 5.

First day sale,

The number of pencils sold on the first day = x ⇒ 5 pencils

The number of notebooks sold on the first day = 2x ⇒ 10 notebooks

Second day sale,

The number of pencils sold on the second day = 2y ⇒ 10 pencils

The number of notebooks sold on the second day = 7y ⇒ 35 notebooks.