Question

How do you solve the system of equations `d+n =70` and `.1d+.05n = 5.5`?

Answer 1

See a solution process below:

Explanation:

Step 1) Solve the second equation for `d`:

`0.1d + 0.05n = 5.5`

`0.1d + 0.05n - color(red)(0.05n) = 5.5 - color(red)(0.05n)`

`0.1d + 0 = 5.5 - 0.05n`

`0.1d = 5.5 - 0.05n`

`color(red)(10) xx 0.1d = color(red)(10)(5.5 - 0.05n)`

`1d = (color(red)(10) xx 5.5) - (color(red)(10) xx 0.05n)`

`d = 55 - 0.5n`

Step 2) Substitute `(55 - 0.5n)` for `d` in the first equation and solve for `n`:

`d + n = 70` becomes:

`(55 - 0.5n) + n = 70`

`55 - 0.5n + n = 70`

`55 - 0.5n + 1n = 70`

`55 + (-0.5 + 1)n = 70`

`55 + 0.5n = 70`

`55 - color(red)(55) + 0.5n = 70 - color(red)(55)`

`0 + 0.5n = 15`

`0.5n = 15`

`color(red)(2) xx 0.5n = color(red)(2) xx 15`

`1n = 30`

`n = 30`

Step 2)

Substitute `30` for `n` in the solution to the second equation at the end of Step 1 and calculate `d`:

`d = 55 - 0.5n` becomes:

`d = 55 - (0.5 xx 30)`

`d = 55 - 15`

`d = 40`

The Solution Is:

`d = 40` and `n = 30`