Question

Jimmy was supposed to multiply a certain number by 43 but by mistake he multiplied that number by 34 as a result his answer was off by 3105. What was the number jimmy was supposed to multiply by 43???

Answer 1

Answer:

345

Step-by-step explanation:

We can solve this problem by two equations. Our variables will be the following:

$x$ is the amount to be multiplied

and $y$ is the amount that should be obtained by multiplying by 43

Thus our first equation is:

$43x=y$

But the problem tells us that there was an error and the number $x$ was multiplied by 34, so the result failed by 3105, thus the second equation is as follows:

$34x=y-3105$

By multiplying the quantity by 34, an amount is obtained that differs from 3105 from what it would have been obtained if multiplied by 43.

Now we are going to replace the first equation in the second one ($y=43x$):

$34x=43x-3105$

And clear to find x:

$3105=43x-34x\\3105=9x\\\frac{3105}{9}=x\\345=x$

The number that jimmy was supposed to multiply by 43 is 345.