Pregunta
The coffee shop Java Jive has prices that increase linearly based on the size of the coffee. The equation below gives the cost \( y \) of a \( x \)-ounce coffee. What size coffee has a cost of \( \$ 4.25 \) ? \( y=0.1 x+2.25 \)
Ask by Deleon Kelley. in the United States
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
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A 20-ounce coffee costs \$4.25 at Java Jive.
Solución
To determine the size of the coffee that costs \$4.25 at Java Jive, we can use the given linear equation:
\[
y = 0.1x + 2.25
\]
Where:
- \( y \) is the cost in dollars.
- \( x \) is the size of the coffee in ounces.
**Step 1: Set the equation equal to \$4.25**
\[
4.25 = 0.1x + 2.25
\]
**Step 2: Subtract \$2.25 from both sides to isolate the term with \( x \)**
\[
4.25 - 2.25 = 0.1x
\]
\[
2.00 = 0.1x
\]
**Step 3: Solve for \( x \) by dividing both sides by 0.1**
\[
x = \frac{2.00}{0.1} = 20
\]
**Conclusion:**
A **20-ounce** coffee costs \$4.25 at Java Jive.
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The Deep Dive
To find the size of the coffee that costs \$4.25, we can set \( y = 4.25 \) in the equation \( y = 0.1x + 2.25 \). \[ 4.25 = 0.1x + 2.25 \] Now, let's solve for \( x \): 1. Subtract 2.25 from both sides: \[ 4.25 - 2.25 = 0.1x \] \[ 2 = 0.1x \] 2. Divide by 0.1: \[ x = \frac{2}{0.1} = 20 \] So, a 20-ounce coffee costs \$4.25! Now you know exactly what size to order when you're craving that perfect cup of java! Imagine the aroma of fresh coffee in your favorite mug as you sip away!
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