Problema Solution
joe has a collection of nickels that is worth 5.30 if the number of dimes was tripled and the number of nickels was increased by 14 the value of the coins would be 8.40 How many nickels and dimes does he have
Answer provided by our tutors
Let x be the number of dimes and y be the number of nickels
You have the following relationships
0.10x + 0.05y = 5.30
0.10(3x) + 0.05(y + 14) = 8.40
Eliminate the decimals: 10x + 5y = 530
10(3x) + 5(y + 14) = 840
10x + 5y = 530
30x + 5y + 70 = 840 --> 30x + 5y = 770
Subtract the equations to eliminate the y: 10x + 5y = 530
30x + 5y = 770
the new equation is -20x = -240 --> x = 12
Then 10(12) + 5y = 530 --> 120 + 5y = 530 --> 5y = 410 --> y = 82
He has 12 dimes and 82 nickels