ABACUS: MYSTERY OF THE BEAD
The Bead Unbaffled - An Abacus Manual

Linear Equations - Gary Flom

Here's another from Gary Flom

I have a handful of dimes and quarters.
There are 28 coins in total.
The total value is $4.45

How many dimes do I have?
How many quarters do I have?

Solution :

Set x = number of dimes
Set y = number of quarters.

The total amount of money is 445 cents.

So we can write eq 1 : 10x + 25y = 445.

And since there are 28 coins in total, we can
write eq 2 : x + y = 28

We solve eq 1 and eq 2 simultaneously.

eq 2 can be written as : y = 28 - x

We will plug this into eq 1 where we see "y".

So now write eq 1 as :

10x + 25(28 - x) = 445

Solve for x :

10x + 700 - 25x = 445

700 - 15x = 445

700 - 445 = 15x

255 = 15x

17 = x

So, we have 17 dimes.

By eq 2 , we now notice y must be 11.

So, we have 11 quarters.

Let's check our answer :

(17 times 10 cents) plus (11 times 25 cents) = 445 cents (checks!)

17 + 11 = 28 coins (checks!)
 

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September 2008
Gary Flom
Totton Heffelfinger