Algebra Word Problem

Question

Paul found $31.85 worth of quarters, nickels dimes in a brown paper bag on the sidewalk.  The ratio of quarters to nickles in the bag was six to eleven and the ratio of quarters to dimes was nine to six.  How many of each type of coin was in the bag.  Round to the ones

Answer 1

1 quarter = $0.25

 

 1 nickel = $ 0.05

 

1 dime =$0.10

 

quarters to nickles = 6:11

quarters to dimes = 9 : 6

so

 

quarters to nickles = 6:11 = 6*6 : 11* 6= 36:66

quarters to dimes = 9 : 6= 9*4 : 6*4 = 36:24

so 

ratio of quarters: nickels:dimes = 36 : 66: 24

                                                  =6:11:4

 

so

0.25(6)k + 0.05(11)k+0.10(4)k=31.85

1.5 k + 0.55k +0.4k = 31.85

2.45k =31.85

k = 13

ratio of quarters: nickels:dimes=6:11:4

no. of quarter = 13*6 = 78

no. of nickel = 13*11=143

no. of dimes = 13*4=52