SOLUTION: 1. I have one-peso coins, 5 peso coins, and 10 peso coins. The total amount that I have is P43. I have 4 times as many 1peso coins as ten peso coins. Altogether, there are 13 coins

Question 1191326: 1. I have one-peso coins, 5 peso coins, and 10 peso coins. The total amount that I have is P43. I have 4 times as many 1peso coins as ten peso coins. Altogether, there are 13 coins. How many of each type of coin do I have? Solve in inverse matrix.
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
I have one-peso coins, 5 peso coins, and 10 peso coins.
The total amount that I have is P43.
I have 4 times as many 1peso coins as ten peso coins.
Altogether, there are 13 coins.
How many of each type of coin do I have? Solve in inverse matrix.
~~~~~~~~~~~~~~

            I will solve it in a better way: I will reduce the problem to one single equation
            in one unknown, and then will solve it.

Let x be the number of 10-peso coins.

Then the number of 1-peso coins is 4x, according to the problem,

and the number of the 5-peso coins is the rest  13-x-4x = 13-5x coins.


Then the total money equation is

    10x + 4x + 5*(13-5x) = 43.


Simplify and find x

    10x + 4x - 25x + 65 = 43

          -11x          = 43 - 65 = -22

             x                    =  = 2.


ANSWER.  There are 2 10-peso coins;  4*2 = 8 1-peso coins and 13-5*2 = 3 5-peso coins.


CHECK.   2*10 + 8*1 + 3*5 = 20 + 8 + 15 = 43 peso, total money.    ! Correct !

Solved.

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