Question

in a school a total of 12 cakes of 1.5 kg each are ordered for the distribution of cakes to the children's. each boy is given 20 grams of a piece of cake and each of the girls is given a piece of 30 grams of cakes. the number of girls in the school is twice the number of boys. find the total number of childrens in the school.
1)525
2)675
3)475
4)650​

Answer 1

The total number of childrens in the school is 675 and the correct answer is option 2) 675.

Given:

In a school a total of 12 cakes of 1.5 kg each are ordered for the distribution of cakes to the children's.

Each boy is given 20 grams of a piece of cake and each of the girls is given a piece of 30 grams of cakes.

The number of girls in the school is twice the number of boys.

To find:

Find the total number of childrens in the school.

Solution:

Let's assume the number of boys in the school is "x".

From the Data, number of girls in the school is twice that, so it would be "2x".

Each boy is given 20 grams of cake, and there are "x" boys, so the total weight of cake for boys is 20 grams × x boys.

Each girl is given 30 grams of cake, and there are "2x" girls, so the total weight of cake for girls is 30 grams × 2x girls.

According to the problem, the total weight of cake ordered is 12 cakes of 1.5 kg each. Therefore,

The total weight of cake ordered

= 12 cakes × 1.5 kg/cake × 1000 grams/kg.

Since the total weight of cake needed for boys and girls should equal the total weight of cake ordered, set up the following equation:

20 grams × x boys + 30 grams × 2x girls = 12 cakes × 1.5 kg/cake × 1000 grams/kg

Let's solve this equation to find the value of "x".

20x + 30 × 2x = 12 × 1.5 × 1000

20x + 60x = 18000

80x = 18000

x = 18000 / 80

x = 225

Therefore, the number of boys in the school is 225, and the number of girls is twice that,

which is 2 × 225 = 450.

To find the total number of children in the school, we add the number of boys and girls: 225 + 450 = 675.

Therefore

The total number of childrens in the school is 675 and the correct answer is option 2) 675.

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Answer 2

The total number of childrens in the school = 675 [ The correct option is 2) 675 ]

Given :

• In a school a total of 12 cakes of 1.5 kg each are ordered for the distribution of cakes to the childrens

• Each boy is given 20 grams of a piece of cake and each of the girls is given a piece of 30 grams of cakes

• The number of girls in the school is twice the number of boys.

To find :

The total number of childrens in the school

1) 525

2) 675

3) 475

4) 650

Solution :

Step 1 of 3 :

Form the equation to calculate number of girls and number of boys

In a school a total of 12 cakes of 1.5 kg each are ordered for the distribution of cakes to the childrens

Total weight of 12 cakes

= 12 × 1.5 kg

= 18 kg

= 18 × 1000 gm

= 18000 gm

Let number of boys = n

Since number of girls in the school is twice the number of boys

∴ Number of girls = 2n

Each boy is given 20 grams of a piece of cake and each of the girls is given a piece of 30 grams of cakes

By the given condition

$\displaystyle \sf (n \times 20) + (2n \times 30) = 1800$

Step 2 of 3 :

Calculate number of girls and number of boys

$\displaystyle \sf (n \times 20) + (2n \times 30) = 1800$

$\displaystyle \sf{ \implies }20n + 60n = 1800$

$\displaystyle \sf{ \implies }80n = 1800$

$\displaystyle \sf{ \implies }n = 225$

Number of boys = n = 225

Number of girls = 2n = 2 × 225 = 450

Step 3 of 3 :

Calculate total number of childrens in the school

Number of boys = 225

Number of girls = 450

Total number of childrens in the school

= 225 + 450

= 675

The total number of childrens in the school = 675

Hence the correct option is 2) 675

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