Question

Two jugs and 4 bottles hold 40 ounces. one jug and 3 bottles hold 25 ounces. how many ounces does 1 jug hold ?

Answer 1

See a solution process below:

Explanation:

Let's call the amount a jug holds" `j`

:Let's call the amount a bottle holds: `b`

From the information in the problem we can write two equations:

• Equation 1: `2j + 4b = 40"oz"`

• Equation 2: `1j + 3b = 25"oz"`

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

`1j + 3b = 25"oz"`

`1j + 3b - color(red)(3b) = 25"oz" - color(red)(3b)`

`j + 0 = 25"oz" - 3b`

`j = 25"oz" - 3b`

Step 2) Substitute `(25"oz" - 3b)` for `j` in the first equation and solve for `b`:

`2j + 4b = 40"oz"` becomes:

`2(25"oz" - 3b) + 4b = 40"oz"`

`(2 xx 25"oz") - (2 xx 3b) + 4b = 40"oz"`

`50"oz" - 6b + 4b = 40"oz"`

`50"oz" + (-6 + 4)b = 40"oz"`

`50"oz" + (-2)b = 40"oz"`

`50"oz" - 2b = 40"oz"`

`50"oz" - color(red)(50"oz") - 2b = 40"oz" - color(red)(50"oz")`

`0 - 2b = -10"oz"`

`-2b = -10"oz"`

`(-2b)/color(red)(-2) = (-10"oz")/color(red)(-2)`

`(color(red)(cancel(color(black)(-2)))b)/cancel(color(red)(-2)) = 5"oz"`

`b = 5"oz"`

Step 3) Substitute `5"oz"` for `b` in the solution to the second equation at the end of Step 1 and calculate `j`:

`j = 25"oz" - 3b` becomes:

`j = 25"oz" - (3 xx 5"oz")`

`j = 25"oz" - 15"oz"`

`j = 10"oz"`

One Jug Holds: `10" ounces"`