Question

(1) The difference between two numbers is 26 and one number is three times the other.
Find them.
The larger of two supplementary angles exceeds the smaller by 18 degrees. Find
them.
m) The coach of a cricket team buys 7 bats and 6 balls for 3800. Later, she buys 3
bats and 5 balls for * 1750. Find the cost of each bat and each ball.​

Answer 1

Answer:

39 and 13

99° and 81°

500 and 50

Answer 2

Answer:

Step-by-step explanation:

i) Let the first (larger) number = x

And the second number = y

The difference between two numbers is 26.

x - y = 26 ....(1)

One number is three times the other

x = 3y ....(2)

Substituting x = 3y in equation (1), we get

3y - y = 26

2y = 26

y = 13

Substituting y = 13 in equation (2)

x = 3 × 13

x = 39

The two numbers are 39 and 13.

(ii) Let the larger angle = x

And the smaller angle = y

Since the angles are supplementary,

x + y = 180 ....(1)

Larger angle exceeds the smaller by 18

x = y + 18 ....(2)

Substituting x = y + 18 in equation (1), we get y + 18 + y = 180

2y = 180 - 18

y = 162/2

y = 81

Substituting y = 81 in equation (2), we get

x = 81 + 18

x = 99

The angles are 99 degrees and 81 degrees.

(iii) Let the cost of 1 bat = ₹ x

And the cost of 1 ball = ₹ y

7x + 6y = 3800 ....(1)

3x + 5y = 1750 ....(2)

By solving equation (1),

7x + 6y = 3800

6y = 3800 - 7x

y = (3800 - 7x) / 6 ....(3)

Substituting y = (3800 - 7x) / 6 in equation (2), we get

3x + 5 [(3800 - 7x) / 6] = 1750

(18x + 19000 - 35x) / 6 = 1750

-17x + 19000 = 1750 × 6

17x = 19000 - 10500

x = 8500/17

x = 500

Substituting x = 500 in equation (3), we get

y = (3800 - 7 × 500) / 6

y = 300/6

y = 50

Cost of 1 bat is ₹ 500

Cost of 1 ball is ₹ 50