Math  /  Algebra

Question8
During the summer, Brendan works on his uncle's dairy farm. One of Brendan's many chores is to load bales of hay onto a wagon and haul them from the field into the barn. \begin{tabular}{|l|l|} \hlinexx (wagon loads) & yy (bales) \\ \hline 1 & 4 \\ \hline 2 & 8 \\ \hline 3 & 12 \\ \hline 5 & 20 \\ \hline \end{tabular}
There is a proportional relationship between the number of wagonloads, xx, and the number of bales of hay Brendan can haul, yy.
Write an equation for the relationship between xx and yy.

Studdy Solution

STEP 1

What is this asking? We need to find the equation that connects the number of wagonloads with the number of bales of hay. Watch out! Make sure your equation works for *all* the given data points, not just one or two!

STEP 2

1. Find the relationship
2. Write the equation

STEP 3

Let's look at the first pair of values: **1** wagonload carries **4** bales.
That's interesting!

STEP 4

The second pair says **2** wagonloads carry **8** bales.
That's **4** bales per wagonload again!

STEP 5

With **3** wagonloads and **12** bales, we still have **4** bales per wagonload! 12÷3=412 \div 3 = 4.

STEP 6

Finally, **5** wagonloads carry **20** bales, and yes, that's 20÷5=420 \div 5 = 4 bales per wagonload!

STEP 7

So, it looks like each wagonload carries **4** bales of hay.
This **rate of change** is consistent across all the data points.

STEP 8

We know that the number of bales, yy, depends on the number of wagonloads, xx.

STEP 9

Since each wagonload carries **4** bales, we can multiply the number of wagonloads by **4** to find the number of bales.

STEP 10

This gives us the equation: y=4xy = 4 \cdot x.

STEP 11

Let's **test** it with our data!
If x=1x = 1, then y=41=4y = 4 \cdot 1 = 4.
Perfect! If x=2x = 2, then y=42=8y = 4 \cdot 2 = 8.
Awesome! It works for all the given values.

STEP 12

The equation that represents the relationship between the number of wagonloads (xx) and the number of bales of hay (yy) is y=4xy = 4 \cdot x.

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