Word Problem

Question

In the nineteenth century, a country minted two-cent and three-cent pieces. Frances Steib has fourfour times as many three-cent pieces as two-cent pieces, and the face value of these coins is $1.82. How many of each denomination does she have?

Answer 1

First identify the values involved
Let x = number of 3-cent coins
Let y = number of 2-cent coins
Then write down the formulas relating them
X = 4y
.03x + .02y = 1.82
Substitute 4y in for x
.03*4y + .02y = 1.82
.12y + .02y = 1.82
.14y = 1.82
Y = 13
Substitute back to solve for x
X= 4 y = 52

Answer 2

X is the # of 3-cent coins

Y is the # of 2-cent coins

 

 X = 4Y

 

 3X + 2Y = 182 <--- amount in pennies to clear away the decimals

 

 3(4Y) + 2y = 182

 

  12Y + 2Y = 182

 

 14Y = 182

 

Y = 182/14 = 13

 

X = 4Y = 4(13) = 52

 

CHECK:

   3(52) + 2(13) = 156 + 26 = 182 <--- YES, the answers are correct

 

13 2-cent coins

52 3-cent coins