Question

The members of the PTA raised some money for the School
Development Fund, in 5 groups. The third group got 600 rupees
more than the first group and 400 rupees more than the second
group. The fifth group got 550 rupees more than the fourth group
and the third group got 200 rupees less than the fourth group.
The fouth group got 4200 rupees. Find the amount raised by each
group. What is the total amount raised for the development fund?​

Answer 1

Total fund raised is 19950 rupees.

Amount raised by group 1 is 3400 rupees.

Amount raised by group 2 is 3600 rupees.

Amount raised by group 3 is 4000 rupees.

Amount raised by group 4 is 4200 rupees.

Amount raised by group 5 is 4750 rupees.

Given: Fourth Group got 4200 rupees.

Third Group got 200 less than fourth group.

First group got 600 rupees less than third group.

Second group got 400 rupees less than third group.

Fifth group got 550 rupees more than the fourth group.

To find: Amount raised by each group.

Solution: By converting the given information in mathematical form we get

STEP 1

$x_{4} = 4200\\x_{3} = x_{4} - 200\\x_{1} = x_{3} - 600\\x_{2} = x_{3} - 400\\x_{5} = x_{4} + 550$

STEP 2

we have the exact value of $x_{4}$ and by putting this in the equation for $x_{3}$ we will get the exact value for $x_{3}$

Therefore,

$x_{3} = 4200 - 200\\x_{3} = 4000$

STEP 3

Now if we will put the value of $x_{3}$ in the equation for $x_{1}$ and $x_{2}$ we will get their exact values.

Therefore,

$x_{1} = x_{2} -600\\x_{1} = 4000 - 600\\x_{1} = 3400$

STEP 4

Now again putting the vale of $x_{3}$ in the equation for $x_{2}$ we get

$x_{2}= x_{3} - 400\\x_{2} = 4000 - 400\\x_{2} = 3600$

STEP 5

Now solving $x_{5}$  by putting the value of $x_{4}$ in the equation of $x_{5}$

$x_{5} = x_{4} + 550\\x_{5} = 4200 + 550\\x_{5} = 4750$

STEP 6

Now we have to find the total amount raised by the development fund. We will calculate it by taking the sum of each individual group.

Therefore,

Total Amount Raised = $x_{1} + x_{2} + x_{3} + x_{4} + x_{5}$

                                   = $3400 + 3600 + 4000 + 4200 + 4750$

                                   = $19950$

To know more about linear equation in one variable refer the link given below:

https://brainly.com/question/2030026

https://brainly.in/question/48534636

#SPJ1