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.

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!