Question

Sally gave her brother $3.95 in quarters and dimes. If the number of quarters is 6 more than the number of dimes, how many quarters did Sally give her brother

Answer 1

First, choose a variable to represent the number of dimes and another variable to represent the number of quarters..

Answer 2

How about let
d = number of dimes
and let
q = number of quarters

Answer 3

Ok so far?

Answer 4

@daniellelynn Are you following?

Answer 5

no to be honest. this is my biggest struggle and im having the worst time understanding

Answer 6

To solve this problem you need a system of equations. A system of equation is 2 or more equations solved together to arrive at an answer.
The first step we need is to let two letters, called variables, represent what we are looking for.

Answer 7

We could use x and y for the variables, but to make it easy to remember what the variables represent, we can let the variable d equal the number of dimes and the variable q equal the number of quarters.

Answer 8

From this statement:
"the number of quarters is 6 more than the number of dimes"
we get:
q = d + 6
This is our first equation.

Answer 9

Now we use the value of the coins and the total to find another equation.

Answer 10

A dime is worth $0.10
A quarter is worth $0.25

Answer 11

d dimes are worth 0.1d
q quarters are worth 0.25q

Answer 12

The problem states:
"$3.95 in quarters and dimes"
That means 0.1d + 0.25q = 3.95
That is our second equation.

Answer 13

Here are the two equations:
q = d + 6
0.1d + 0.25q = 3.95

Answer 14

@daniellelynn oohoo!
@mathstudent55 has been writing for 15 minutes and he would appreciate some response... please!

Answer 15

Since the first equation is already solved for q, we can use substitution.
We replace q of the second equation with what q is equal to in the first equation, d + 6.
0.1d + 0.25(d + 6) = 3.95
Distribute the 0.25:
0.1d + 0.25d + 1.5 = 3.95
Add 0.1d and 0.25d together. Subtract 1.5 from both sides:
0.35d = 2.45
d = 7
There are 7 dimes.
Since the number of quarters is 6 more than dimes, there are 7 + 6 = 13, 13 quarters.

Answer 16

Another method to solve this problem:

You can always set up a system of linear equations with 2 unknowns and then solve the system, as @mathstudent55 has clearly explained.

However, if you want to do it in your head, this is what you could do.
1. There are \(6~~more~~quarters\) than dimes, so if we take away the 6 quarters, we can subtract 6*$0.25=$1.50 from the total, we are left with $2.45 with equal number of quarters and dimes.
2. Divide $2.45 by (0.25+0.10)=0.35 gives 7.
3. So there are 7 dimes and (7+6)=13 quarters.

Answer 17

thank you for the help! thank you so much!!