# Algebra

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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 -

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 -

Thanks a lot!

• Algebra -

You are welcome,
did you get the 2nd question?

• Algebra -

Oh yes! I figured it out by myself.

• Algebra -

good job

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