Question

The sum of 3 numbers 88 the 2nd number is 5 times of one fourth of the first number and the 3rd number is 10 more than the 1st number. Find the three numbers​

Answer 1

Answer:-

Given:-

Sum of three numbers = 88

Let, the numbers be x , y and z.

⟹ x + y + z = 88 -- equation (1)

And,

The 2nd number is 5 times of one fourth of the first number.

i.e., y is 5 times of one fourth of x.

⟹ y = 5 * (1/4) * x

⟹ y = 5x/4 -- equation (2)

Also,

The third number is 10 more than the first number.

i.e., z is 10 more than x.

⟹ z = x + 10 -- equation (3)

Now, substitute y = 5x/4 & z = x + 10 in equation (1)

⟹ x + 5x/4 + x + 10 = 88

⟹ (4x + 5x + 4x)/4 = 88 - 10

⟹ 13x/4 = 78

⟹ x = 78*4/13

⟹ x = 24

Substitute x = 24 in equation (2)

⟹ y = 5(24)/4

⟹ y = 5 * 6

⟹ y = 30

Substitute x = 24 in equation (3)

⟹ z = 24 + 10

⟹ z = 34

∴ The three required numbers are 24 , 30 & 34.

Answer 2

Information provided with us :

• The sum of 3 numbers 88
• The 2nd number is 5 times of one fourth of the first number
• The 3rd number is 10 more than the 1st number.

What we have to calculate :

• Those three numbers

Performing Calculations :

• Let us assume the three unknown numbers as an variable. We are assuming a , b and c those numbers which were added.

$: \longmapsto \: \sf{a \: + \: b \: + \: c \: = \: 88}$

• Now in the question it is given that 2nd number is 5 times of one fourth of the first number. We know that 2nd number is b and first number is a. So we would multiply the first number that is a by 1/4.

$: \longmapsto \: \sf{b \: = \: 5\bigg( \dfrac{1}{4}\bigg) \: \times a}$

$: \longmapsto \: \sf{b \: = \: 5 \times \dfrac{1}{4} \: \times a}$

$: \longmapsto \: \sf{b \: = \: \dfrac{5}{4} \: \times a}$

$: \longmapsto \: \boxed{\sf{b \: = \: \dfrac{5a}{4} }}$

• Now in the question it is given that 3rd number is 10 more than the 1st number. We know that 3rd number is c and 1st number is a. So we would be adding 10 to the first number.

$: \longmapsto \: \sf{c \: = \: a \: + \: 10}$

Putting the values of b and c :

$: \longmapsto \: \sf{a \: + \: \dfrac{5a}{4} \: + (a + 10) = \: 88 }$

$: \longmapsto \: \sf{a \: + \: \dfrac{5a}{4} \: + a + 10 = \: 88 }$

$:\longmapsto \: \sf{2a \: + \: \dfrac{5a}{4} \: + 10 = \: 88 }$

$:\longmapsto \: \sf{2a \: + \: \dfrac{5a}{4} \: = \: 88 - 10}$

$:\longmapsto \: \sf{2a \: + \: \dfrac{5a}{4} \: = \: 78}$

$:\longmapsto \: \sf{ \dfrac{8a + 5a}{4} \: = \: 78}$

$:\longmapsto \: \sf{ \dfrac{13a}{4} \: = \: 78}$

$:\longmapsto \: \sf{13a\: = \: 78 \times 4}$

$:\longmapsto \: \sf{13a\: = \: 312}$

$:\longmapsto \: \sf{a\: = \: \dfrac{312}{13} }$

$:\longmapsto \: \sf{a\: = \: \cancel\dfrac{312}{13} }$

$:\longmapsto \: \boxed{\red{\bf{a\: = \: 24}}}$

Finding out the value of b :

$:\longmapsto \: \sf{b\: = \: 5 \bigg(\dfrac{24}{4} \bigg) }$

$:\longmapsto \: \sf{b\: = \: 5 \bigg( \cancel\dfrac{24}{4} \bigg) }$

$:\longmapsto \: \sf{b\: = \: 5 \times 6}$

$:\longmapsto \: \red{\boxed{\bf{b\: = \: 30}}}$

Finding out the value of c :

$:\longmapsto \: \sf{c\: = \: 24 + 10}$

$:\longmapsto \: \boxed{\red{\tt{c\: = \: 34}}}$

$\underline{\bf{Henceforth, \: three \: numbers \: are \: 24, \: 30 \: and \: 34}}$