Question

Barney and Betty break into a parking meter with $5.05 in dimes and quarters in it, and agree that Barney get all the dimes, and Betty will get all the quarters. Barney ends up with five more coins than Betty. How much money did each get?

Answer 1

The question is about solving a system of linear equations to find out how much money from the parking meter Barney and Betty each get, by determining the number of dimes and quarters they collected.

Step-by-step explanation:

The student's question involves solving a system of linear equations. Barney and Betty break into a parking meter containing $5.05 in dimes and quarters, with Barney getting all the dimes and Betty all the quarters, and Barney ends up with five more coins than Betty. We know that a dime is worth $0.10 and a quarter is worth $0.25.

Let's let D be the number of dimes and Q be the number of quarters. The first equation comes from the total amount of money:

1. 0.10D + 0.25Q = 5.05

The second equation comes from the difference in the number of coins:

2. D = Q + 5

Now, we'll solve this system of equations, typically by substitution or elimination method. Solving these will give us the exact number of dimes and quarters, and consequently how much money each person gets.

Answer 2

so remember that a quarter=25 cents and a dime=10 cents so
represent q=# of quarters
d=# of dimes

so barney gets dimes so replace barney with d and betty with q
barney get 5 more coins than betty
d=5+q
total=5.05=0.25q+0.10d since each is worth 0.25 and 0.10 so we have
d=5+q and 5.05=0.25q+0.10d
subsitue (5+q) for d
5.05=0.25q+0.10(5+q)
distribute
5.05=0.25q+0.50+0.10q
add like terms
5.05=0.35q+0.50
subtract 0.50 from both sides
4.55=0.35q
divide both sides by 0.35
13=q
subsitute
d=5+q
d=5+13
d=18

barney got 18 coins and betty got 13 coins