Question 275466
Joe has a collection of nickels and dimes that is worth $6.65.  If the number of dimes were doubled and the number of nickels were increased by 11, the value of the coins would be $11.60.  How many dimes does he have?


let the number of nickel coins be x
let the number of dimes be y

5x+10y =665 cents

nickels were increase by 11 so it becomes x+11

Dimes were doubled so it beomes 2y 

5(x+11)+10*2y = 1160 cents
5x+55+20y= 1160
5x+20y = 1160-55
5x+20y= 1105

5x+20y= 1105----------1
5x+10y =665 ----------2

subtract equation 2 from equation1

10y= 440
y= 44 = Number of dimes.

Number of nickels will be 

5x+10y =665  put the value of y in the equation

5x+440 = 665
5x= 665-440

5x=225
x=45 number of nickels

2. Ellen wishes to mix candy worth $1.98 per pound with candy worth $3.96 per pound to form 20 pounds of a mixture worth $2.87 per pound.  How many pounds of the more expensive candy should she use?

$1.98 candy--------------- $3.96 candy------------- $2.87 candy mix
x------------------------- 20-x----------------------20 pounds

The value of these two added should be equal to the value of the mixed candy

1.98x+3.96(20-x) = 20*2.87

1.98x+79.20 - 3.96x= 57.4

-1.98x= 57.4-79.2
-1.98x=-21.8
x= -21.8/-1.98
x=11 pounds which is $1.98 candy
$3.96 candy added will be 20-11=9 pounds