Question

Two teachers A and B went to a 'Sale' to purchase geometry box 4
and notebooks for the prize distribution in Mathematics Quiz which
will be organized next week in the school. The number of geometry
box is one less than the number of notebooks purchased. Also, the
three times number of geometry box is 12 more than two times
the number of notebooks purchased".
Based on the above layout and situation, answer the
following questions:
Form the pair of linear equations in two variables from
this situation.
How many geometry boxes and notebooks teachers
bought for the school?​

Answer 1

$\gray{\underline{\mathbb{\blue{ANSWER:}}}}$

• Pair of linear equations in two variables are x = y - 1 and 3x = 2y + 12 .

• Number of geometry boxes = 14 and the number of notebooks = 15

$\gray{\underline{\mathbb{\red{GIVEN:}}}}$

• The number of geometry boxes is one less than the number of notebooks purchased.

• Three times number of geometry boxes is 12 more than two times the number of notebooks purchased.

$\gray{\underline{\mathbb{\green{TO \ FIND:}}}}$

• Pair of linear equations in two variables.

• Number of geometry boxes and notebooks teachers bought for the school.

$\gray{\underline{\mathbb{\purple{EXPLANATION:}}}}$

Let the number of geometry boxes be x and notebooks be y.

Linear equations:

x = y - 1

3x = 2y + 12

Number of geometry boxes and notebooks bought:

Substitute x = y - 1 in 3x = 2y + 12

3(y - 1) = 2y + 12

3y - 3 = 2y + 12

y = 15

Substitute y = 15 in 3x = 2y + 12

3x = 2(15) + 12

3x = 30 + 12

3x = 42

x = 14

Number of geometry boxes = 14 and the number of notebooks = 15.

$\gray{\underline{\mathbb{\orange{VERIFICATION:}}}}$

Substitute x = 14, y = 15 in x = y - 1

14 = 15 - 1

14 = 14

Substitute x = 14, y = 15 in 3x = 2y + 12

3(14) = 2(15) + 12

42 = 30 + 12

42 = 42

HENCE VERIFIED.