Question

A friend tells you that she has been saving every 5- dollar and every 10 - dollar bill she has received for the last year . She now has 80 bills for a total of $550.00 . How many 5 - dollar bills and how many 10 - dollar bills does she have ? 1 . Write an equation . 2 . Use graphing , substitution or elimination to solve the system of equations . 3 . How many 5- dollar bills and how many 10 - dollar bills does she have ? 4 . Explain why your answer is correct . 5 . Explain why you chose the method .

Answer 1

Answer is in the explanation.

Step-by-step explanation:

Let's make a system of equations.

5x+10y=550

x+y=80

Now let's use elimination

-5x-5y=-400

5x+10y=550

__________

5y=150

y=30

Then subsitute 30 in for y to find x. This will leave you with x=50. You will have 50 $5 bills and 30 $10 bills. You can check by subsituting x for 50 and y for 30 in both equations to show why it is correct. Eliminating makes it easier to solve the system of equations.

Answer 2

1. The equations are
`x+y=80 \ and \ 5x+10y=550`

2. we can use elimination method to solve the problem

3. She has 50 5$ bills and 30 10 $ bills

4. The values of x and y that we found satisfies the two equations which ensures that the solution is correct.

5. Elimination method involves lesser number of steps when compared with graphical method and substitution method.

Step-by-step explanation:

Number of 5$ bills=x

Number of 10$ bills=y

Total number of bills=80

`x+y=80`

total amount=$550

`5x+10y=550`

Here we have two equations and we can use elimination method to solve the set of equations

`x+y=80` (Equation 1)

`5x+10y=550` (Equation 2)

We have to make the coefficient of one variable in both equations same.

Let us make the coefficient of x same.

`(1) * 5 => 5x+5y=400` (Equation 3)

Subtract (3)from (2)

`5x+10y-(5x+5y)=550-400`

`5x+10y-5x-5y=150`

`5y=150`

`y=150/5=30`

Substitute the value of y in equation (1)

`x+y=80`

`x+30=80`

`x+30=80`

`x=80-30=50`

x=50

y=30