Question

​10.​Forty-five children attend a preschool. The number of two-year-olds is one half the number of three-year-olds. The number of four-year-olds is the same as the number of three-year-olds. ​a.​How many two-year-olds attend the preschool? ​b.​How many three-year-olds attend the preschool? ​c.​How many four-year-olds attend the preschool?

Answer 1

Answer:

• 9 two-year-old kids attend the preschool.
• 18 three-year-old kids attend the preschool.
• 18 four-year-old kids attend the preschool.

Step-by-step explanation:

Given that:

• 45 students attend a preschool.
• The number of 2 year old kids is half the number of 3 year old kids.
• The number of 4 year old kids is the same as the number of 3 year old kids.

To Find:

• How many 2 year old kids attend the preschool?
• How many 3 year old kids attend the preschool?
• How many 4 year old kids attend the preschool?

Let us assume:

• Number of 3 year old kids is x.

Then,

• Number of 2 year old kids will be x/2.
• Number of 4 year old kids will be x.

According to the question:

No. of 2 year old kids + No. of 3 years old kids + No. of 4 year old kids = 45

Substituting the values,

$\sf{\longrightarrow x+x+\dfrac{x}{2}=45}$

Adding the variables,

$\sf{\longrightarrow \dfrac{2x+2x+x}{2}=45}$

$\sf{\longrightarrow \dfrac{5x}{2}=45}$

Transposing 2 from LHS to RHS and changing its sign,

$\sf{\longrightarrow 5x=45\times2}$

Multiplying the numbers,

$\sf{\longrightarrow 5x=90}$

Transposing 5 from LHS to RHS and changing its sign,

$\sf{\longrightarrow x=\dfrac{90}{5}}$

Dividing the numbers,

$\sf{\longrightarrow x=18}$

Hence,

• x = 18

Therefore,

• No. of 2 year old kids = x/2 = 18/2 = 9
• No. of 3 year old kids = x = 18
• No. of 4 year old kids = x = 18