Dennis mowed his next door neighbor's lawn for a handful of dimes and nickles, 80 coins in all. upon completing the job he counted out the coins and it came to $6.60. how many of each coin did he earn?

28 nickels and 58 dimes

Step-by-step explanation:

This situation has two unknowns - the total number of dimes and the total number of nickels. Because we have two unknowns, we will write a system of equations with two equations using the two unknowns.  

• is an equation representing the total number of coins

• is an equation representing the total value in money based on the number of coin. 0.10 and 0.05 come from the value of a dime and nickel individually.

We write the first equation in terms of n by subtracting it across the equal sign to get . We now substitute this for d in the second equation.

After simplifying, we subtract 8 across and divide by the coefficient of n.

We now know of the 80 coins that 28 are nickels. To find the total number of dimes, we subtract 28 from 80 to get 52 dimes.

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.