Question

You have $8.80 in Pennie’s and nickels you have twice as many nickels as pennies write a system of linear equations that model the situation how many coins do you have

Answer 1

Explanation:

Let p be the number of pennies and n be the number of nickels. As you have $8.80 in total (given that pennies are worth $0.01 and nickels are worth $0.05)

0.01p + 0.05n = 8.80

You also know that there are twice as many nickels than pennies (or alternatively, there are 2 nickels for every penny).

n = 2p

You can substitute this value of n into the first equation

0.01p + 0.05n = 8.80

0.01p + 0.05(2p) = 8.80

0.01p + 0.10p = 8.80 (multiplying out the brackets)

0.11p = 8.80 (collecting the p's)

p = 80

Putting this back into the second equation

n = 2p

n = 2(80) = 160

So there are 160 nickels and 80 pennies.

You can put this back into the first equation to check it.

0.01p + 0.05n = 8.80

0.01(80) + 0.05(160) = 0.80 + 8 =8.80