Question

There are 14 red and 9 blue balls in a basket. The total weight of the blue and red balls is 128.61g A blue ball is 2.79g heavier than a red ball. Find the weight of a blue ball​

Answer 1

Step-by-step explanation:

Given :-

There are 14 red and 9 blue balls in a basket.

The total weight of the blue and red balls is 128.61g .

A blue ball is 2.79g heavier than a red ball.

To find :-

The weight of a blue ball.

Solution :-

Let the weight of the red ball be X g

Number of red balls = 14

Total weight of all 14 red balls

= 14×Xg = 14X g

The weight of the blue ball

= 2.79g heavier than a red ball

= (X+2.79)g

The weight of a blue ball = (X+2.79) g

Number of blue balls = 9

Total weight of all 9 blue balls

= 9×(X+2.79) g

= (9X + 25.11) g

Total weight of all 9 blue balls = (9X+25.11) g

Total weight of all blue and red balls

= (9X+25.11)+14X

= 9X+14X+25.11

= (23X+25.11) g

According to the given problem

The total weight of the blue and red balls

= 128.61 g

Therefore, 23X+25.11 = 128.61

=> 23X = 128.61-25.11

=> 23X = 103.50

=> X = 103.50/23

=> X = 4.5 g

The weight of each red ball = 4.5 g

The weight of each blue ball

= ( X+2.79 ) g

= 4.5 +2.79 g

= 7.29 g

Answer:-

The weight of each blue ball = 7.29 g

Check :-

The weight of each red ball = 4.5 g

The weight of all 14 red balls

= 14×4.5 g = 63 g

The weight of each blue ball = 7.29 g

The weight of all 9 blue balls

= 9×7.29 g = 65.61 g

Total weight of all blue and red balls

= 65.61 g + 63 g

= 128.61 g

Verified the given relations in the given problem.

Answer 2

Information provided with us:

• There are 14 red and 9 blue balls in a basket.

• The total weight of the blue and red balls is 128.61 gram

• A blue ball is 2.79 gram heavier than a red ball.

What we have to find :

• The required weight of a blue ball

Assumption :

• ➡Consider weight of red ball = r

• ➡ Consider weight of blue ball = b

According the 1 st condition,

• ➡ The total weight of the blue and red balls is 128.61 gram

$\rm \longrightarrow \: 14 \: r + \: 9 \: b = 128.61$

According the 2 nd condition,

• ➡ The blue ball is 2.79 gram heavier than a red ball

$\rm \longrightarrow \: b = \: r + 2.79$

Calculation :

• ➡ Place the value of b = r + 2.79 in 14 r + 9 b = 128.61

$\rm \longrightarrow \: 14 \: r + 9 \times (r + 2.79) = 128.61$

$\rm \longrightarrow \: (14 \: r + 9r) + 25.11 = 128.61$

$\rm \longrightarrow \: 23 \: r = 128.61 - 25.11$

$\rm \longrightarrow \: 23 \: r = 103.5$

$\rm \longrightarrow \: \: r = \dfrac{103.5}{23}$

$\bf \longrightarrow \: \: r = 4.5 \: gram$

Now ;

• ➡ Again by using substitution method Substitute the value of r = 4.5 in b = r + 2.79

$\rm \longrightarrow \: \: b =( 4.5) + 2.79$

$\bf \longrightarrow \: \: b = 7.29\: gram$

Therefore :

• ➡The required weight of a blue ball is 7.29 gram