Question

Amit's school is an unusual school. It has 1677 in grades 3-6. There are twice as many fifth gradersas sixth graders and three times as many fourth graders as fifth graders. Finally,there are five times as many third graders as fourth graders.How many fiftj graders in Amit's school

Answer 1

Answer:

There are 86 fifth graders in Amit's school.

Step-by-step explanation:

Given:

Total number of students from 3-6 = 1677

We need to find the number of fifth graders in Amit's school.

Solution:

Let the number of sixth graders be $'x'$.

Now given:

There are twice as many fifth graders as sixth graders.

Number of fifth graders = $2x$

Also Given:

three times as many fourth graders as fifth graders.

So we can say that;

Number of fourth graders is equal to three times number of fifth graders.

framing in equation form we get;

Number of fourth graders = $3\times2x=6x$

Also Given:

there are five times as many third graders as fourth graders.

So we can say that;

Number of third graders is equal to 5 times number of fourth graders.

framing in equation form we get;

Number of third graders = $5\times6x=30x$

Now we can say that;

Total number of students from 3-6 is equal to number of sixth graders plus Number of fifth graders plus Number of fourth graders plus Number of third graders.

framing in equation form we get;

$x+2x+6x+30=1677\\\\39x=1677$

Dividing both side by 39 we get;

$\frac{39x}{39}=\frac{1677}{39}\\\\x=43$

Number of sixth graders = 43

Number of fifth graders = $2x=2\times43 = 86$

Number of fourth graders = $6x=6\times43 = 258$

Number of third graders = $30x= 30\times43 = 1290$

Hence There are 86 fifth graders in Amit's school.