Question

7. If 45 is subtracted from twice the greater of two numbers, it results in
the other number. If 21 is subtracted from twice the smaller number, it
results in the greater number. Find the numbers.

Answer 1

★Given:-

• If 45 is subtracted from twice the greater of two numbers it results in  the other number.
• If 21 is subtracted from twice the smaller number, it  results in the greater number.

★To find:-

• Find the numbers.

★Solution:-

Let x be greater number and y be smaller number.

According to question,

➜2x - 45 = y

➜2x -  y = 45 ……….(i)  

➜2y - 21 = x

➜-x +2y = 21 ………(ii)

Multiplying equation(i) by 2,

➜4x - 2y = 90 ………..(iii)  

Adding equation(ii) & (iii),

-x +2y = 21

4x - 2y = 90

3x + 0 = 90+21

➜3x = (90 + 21) = 111  

➜x = 111/3

➜x = 37  

Therefore,the greater number is 37.

Substituting value of x in equation(i),

➜2x -  y = 45

➜2(37)- y = 45  

➜74 - y = 45

➜y = (74 - 45)

➜y = 29

Hence,the numbers are 37 & 29.

_____________

Answer 2

Question:-

1) If 45 is subtracted from twice the greater of two numbers, it results in

the other number. If 21 is subtracted from twice the smaller number, it

results in the greater number. Find the numbers.

Answer:-

✔ x, y

✔ x > y

✔ 2x - 45 = y

✔ 2x - 21 = x

✔ 2y = x + 21

✔ y = $\rm \frac{x+21}{2}$

✔ 2x - 45 = $\rm \frac{x+21}{2}$

✔ 4x - 90 = x + 21

✔ 3x = 90 + 21

✔ x = 30 + 7 =37

✔ x = 37

✔ y = $\rm \frac{37+21}{2}=\frac{58}{2}=29$

✔ 37,29

Required answer:-

• 37,29