Question

A man has a box of coins that he uses when playing poker with friends. The box currently contains 42 coins, consisting of pennies, dimes, and quarters. The number of pennies is equal to the number of dimes, and the total value is $3.87. How many of each denomination of coins does he have? Let x represent the number of pennies. Complete the table. Denomination (in dollars) Value Number of Coins (in dollars) Pennies 0.01 0.01x Dimes Quarters 0.25 3.87

Answer 1

Pennies , dimes and quarters are worth 1, 10 and 25 cents respectively.

Let the number of pennies , dimes and quarters in the box be x,y,z respectively.

Then x+y+z = 42…(1).

Also y = x . so that the 1^st equation changes to 2x+z = 42 …(2).

Further, the total value of the coins is 0.01x+0.10x+0.25z = 0.11x+0.25z so that 0.11x+0.25z = 3.87 or, 11x+25z= 387…(3).

The augmented matrix of the above linear system is A (say) =

2	1	42
11	25	387

The RREf of A is

1	0	17
0	1	8

This implies that x = 17 and z = 8.

Thus, there are 17 pennies, 17 dimes and 8 quarters in the box.