I have ten coins made up of 5 peso and 10 peso coins, if these ten coins are worth 70 pesos

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Question: I have ten coins made up of 5 pesos and 10 pesos coins, if these ten coins are worth 70 pesos, how many more 5 peso coins than 10 coins do I have?

Answer: We have two equations for the problem.

Let:

F= number of five peso coins
T= number of ten peso coins

1st equation:  F + T = 10 (from “I have ten coins)
2nd equation: 5F + 10T = 70 (from “These ten coins are worth 70)

5* (F + T) = 5F + 5T = 50

Subtract this from 5F + 10T :

5F + 10T – 5F – 5T = 5T = 70 – 50 = 20
5T = 20 ⇒ T = 4
F + T = 10 ⇒ F + 4 = 10 ⇒ F = 6

You have two more five peso coins (6) than ten peso coins (4).

Check: 4*10 + 6*5 = 40 + 30 = 70

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