Decimals-Increase & Decrease?

The correct answer should be $3650 as you know (or hopefully the book has this as the answer).

Here's how you can do it:

Call the amount of the budget last year x dollars

6% of x dollars would be .06x

This represents how much of the budget is being cut. So subtract this from last years budget:

x - .06x = .94x

.94x represents the current budget, which is $3431. So:

.94x = 3431

Divide by .94. 3431/.94 = $3650.

I hope this helps.

Another way to look at it:

If the budget is cut by 6%, that means that you get to keep 94%.

That means:

$3431 is 94% of last year.

3431 = .94 * last year (divide by .94 and you get the same result as above)

When the budget get reduced by 6% it means that if your budget was $100 the previous year,this year it is $ 94

If you want to solve the problem with the help of fraction,multipky this year's budget by 100/94,

Last year's budget was

100/94 of 3431

=100/94*3431

=$3650

If however. you want to solve it with decimals,we may say that it was reduced by 6% or 0.06 and hence if it was $1.00 the earlier year,it is $1,00-$0.06 or $0.94 this year.

Hence the budget last year was ( 1.00/0.94)

multiplied by $3431

And if you forget every thing,here is the easiest wayof solving it

Let the amount of budget be $x last year.

Therefore the budget is $0.94x this year

By the problem,

0.94x=3431

=>x=3431/0.94 [dividing both sides by0.94]

=>x=$3650

Hope it helps

Opps - read your problem wrong -

Your problem is to find what number, when reduced by 6%, equals 3431. As an equation, it becomes

x(1-0.06) = 3431 ==

x(0.94) = 3431

x = 3431/.94 = 3650

What you're doing is multiplying by 1.06 - although that may initially seem like the way to get a correct answer, that isn't quite the way to do it.

.

Lets say X = last years budget. Then the formula:

X * (1.0 - 0.6) = 3431 would represent the 6% reduction this year.

Solving for X you get:

X = 3431 / 0.94 = 3650.

I get 3650. Here's how: 3431/0.94 = 3650. It seems like your way (3431 X 1.06) would work, but it's going the wrong way, so to speak. But, if you multiply 3650 by 0.94 it works. You can check by multiplying 3650 by 0.06, then subtracting that from 3650, and that comes out to 3431.60. If you multiply your answer by .06 and then subtract it from your original you'll find it doesn't work. So...checking the result is the best way to see if it is right, and in this case there are only two ways to arrive at an answer.

The budget last year was x. Then they decreased it by 6%, that means the budget this year is

x-0.06x=(1-0.06)x=0.94 x= 3431

dividing both sides of

0.94 x = 3431

by 0.94, you get that x = 3650.

There's no easy way to undestand how to do everything... but taking problems one at a time, and thinking about them really helps. It's never wasted time.

Best, and good luck!

Let x = last year's budget

Then .94x = this year's budget.

So .94x = $3431

x = $3431/.94 = $3650