Question

Flour costs $0.75 per pound and sugar costs $0.50 per pound. An order of flour and sugar weighs 16 pounds and costs $9.
Start by substituting 16−s for f in the first equation.
0.75f+0.5s=9
f=16−s
0.75f+0.5s
=
9

0.75(
)+0.5s
=
9

Answer 1

To substitute \( f = 16 - s \) into the equation \( 0.75f + 0.5s = 9 \), we'll replace \( f \) in the cost equation with \( 16 - s \).

Starting with the equation:

\[
0.75f + 0.5s = 9
\]

we substitute \( f \):

\[
0.75(16 - s) + 0.5s = 9
\]

Now we'll distribute \( 0.75 \):

\[
0.75 \cdot 16 - 0.75s + 0.5s = 9
\]

Calculating \( 0.75 \cdot 16 \):

\[
12 - 0.75s + 0.5s = 9
\]

Now, combine the \( s \) terms:

\[
12 - 0.25s = 9
\]

Next, isolate \( -0.25s \) by subtracting 12 from both sides:

\[
-0.25s = 9 - 12
\]
\[
-0.25s = -3
\]

Now, divide both sides by \(-0.25\):

\[
s = \frac{-3}{-0.25} = 12
\]

Now that we have \( s = 12 \), we can find \( f \):

\[
f = 16 - s = 16 - 12 = 4
\]

To summarize:
- Flour \( f = 4 \) pounds
- Sugar \( s = 12 \) pounds

Let's verify that these values satisfy both the weight and cost equations:

1. **Weight**: \( f + s = 4 + 12 = 16 \) (Correct)
2. **Cost**: \( 0.75f + 0.5s = 0.75(4) + 0.5(12) = 3 + 6 = 9 \) (Correct)

The values are verified as correct: \( f = 4 \) pounds of flour and \( s = 12 \) pounds of sugar.