Posted by Summer on Thursday, November 7, 2013 at 7:44pm.
1.The ratio of nickels to dimes to quarters in 3 : 8 : 1. If all the coins were dimes, the amount of money would be the same. Show that there are infinitely many solutions to this problem.
2.A grocer wants to make a mixture of three dried fruits. He decides that the ratio of pounds of banana chips to apricots to dates should be 3:1:1. Banana chips cost $1.17/lb, apricots cost $3.00/lb, and dates cost $2.30/lb. What is the cost per pound of the mixture?

Algebra  Reiny, Thursday, November 7, 2013 at 9:01pm
number of nickels = 3x
number of dimes = 8x
number of quarters = x
value of the money = 5(3x) + 10(8x) + 25x = 120x
number of coins = 12x
suppose we have 12x dimes as stated
value of all the those 12x dimes = 10(12x) = 120x
so 120x = 120x
0 = 0 !!!!!
the variables dropped out and the remaining statement is true.
Therefore, there are infinitely many solutions
btw, if the variables drop out, and the remaining statement is false, such as 5 = 9, there would be NO solutions to the problem 
Algebra  Summer, Thursday, November 7, 2013 at 9:10pm
Thanks a lot!

Algebra  Reiny, Thursday, November 7, 2013 at 9:14pm
You are welcome,
did you get the 2nd question? 
Algebra  Summer, Thursday, November 7, 2013 at 9:22pm
Oh yes! I figured it out by myself.

Algebra  Reiny, Thursday, November 7, 2013 at 9:30pm
good job