Mike went to a store and spent half his money. Now he has as many pennies as he had dollars before, but only half as many dollars as he had pennies before. How much did he spent?

Question

anonymous · Answer

*spend

anonymous · Answer

(100)d  +  p  =  m          and       (1/2)(100)p  +  d  =  (1/2)m

multiply the second equation by 2 and set the left sides of both equations equal to each other.  Establish a ratio of d/p and you will get the original amount of dollars and pennies and from that original amount of money you can divide by 2.

anonymous · Answer

Am I supposed to solve the frat equation for p and plug into the second equation?

anonymous · Answer

First* not frat

anonymous · Answer

This type of problem is a bit different from the usual "2 equations in 2 variables" because you have a third variable "m" for money.  So, this type of problem has to use proportions.  It won't be that hard.  Once you follow the directions in the first post exactly, you will get one equation in 2 variables (d and p).  That's why you have to use a proportion.  Work half of the first post out, and if you get that far and are still stuck, I'll help you finish it.

anonymous · Answer

Start by multiplying the second equation (both sides) by 2.

anonymous · Answer

If you want help on this problem, you'll have to come back because I'm going to have to leave soon, @Skip2mylou426

anonymous · Answer

So if I multiply the second equation by 2, I get 100p+2d=m

anonymous · Answer

That's good.  Now set the left side of that equal to the left side of equation #1.  That is permissible because both equal "m".

anonymous · Answer

Ok, so 99p=98d

anonymous · Answer

Very good.  Establish a ratio of d to p.  I'd use the fraction d/p equal to something, from what you just typed.

anonymous · Answer

d/p=99/98

anonymous · Answer

Very good.  What we have is of course a ratio.  But we can use that ratio as actual values of d and p.  In other words, we can take as our original # of dollars to be 99 and our original # of pennies to be 98.   That gives use $99.98 to start with.  Notice what happens when you divide that by 2.

anonymous · Answer

So,  $99.98 divided by 2 is $49.99   

Notice the switch of 99.

anonymous · Answer

And 49 is half of 98.  And that fulfills the requirements of the problem.

anonymous · Answer

Gotcha! Thank you for your help!

anonymous · Answer

This was actually a very fun problem.  That's if you like this type of fun!

uw!