Question

The sum of 2 nos is 4000 . If 15 % of one is equal to 25% of the other no. Find the nos ?

Answer 1

The numbers are `x=2500` and `y=1500`.

Explanation:

Let x and y be the two numbers.

First equation:
`x+y=4000`

Second equation (remember `15%` of a number means `.15` times the number):
`.15x=.25y`

Isolate y in the first equation:
`x+y=4000`
`y=4000-x`

Substitute this into the second equation:
`.15x=.25(4000-x)`
Distribute and solve for x:
`.15x=1000-.25x`
`.4x=1000`
`x=2500`

Substitute this into first equation written in terms of y:
`y=4000-x`
`y=4000-(2500)`
`y=1500`

Answer 2

`a=2500" "b=1500`

Explanation:

Let one value be represented as `a`
Let the other letter be represented as `b`

Then we have `a+b=4000`...Equation(1)

Also we have:

`15/100a=25/100b`

`=>a=25/(cancel(100))xx(cancel(100))/15 b`

`a= 5/3b` ......................................Equation(2)
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`color(blue)("Determine the value of "b)`

substitute for `a` in equation(1) using equation(2)

`a+b=4000" "->" "5/3b+b=4000`

`8/3b=4000`

`b=3/8xx4000`

`color(blue)(b=1500)`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the value of "a)`

`color(blue)(a=4000-1500 = 2500)`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Check")`

`15/100a" "=25/100b`

Consider the LHS
`15/100xx2500 = 375`

Consider the RHS
`25/100xx1500=375`

`LHS=RHS" "` so correct