Question

3. A grocery store worker has to collect all the shopping carts left out in the parking
lot. He collects 4 carts and measures the length of the 4 carts he is pushing to be
51 inches. He collects another cart for a total of 5 carts and measures the length of
the 5 carts to be 57 inches.
153in
a. He sees that there are a total of 21 carts in the parking lot. How long will the line
of 21 carts be?
b. If he is pushing a line of carts that is 117 inches long, how many carts does he
have?
33+(n-1) x6 =117
6n-6 =117-33
+6
6n=90
واؤ
+6
6n=90
c. How long is a single cart?
33 inches long. 74
6 = 15 carts

Answer 1

By finding a linear equation, we conclude that the length of 21 carts is 153 in

How long will be the line of 21 carts in the parking lot?

Here we know that:

• A line of 4 carts measures 51 inches.
• A line of 5 carts measures 57 inches.

Now, the relation between the length L and the number of carts x must be a linear relation:

L = a*x + b

Where a is the slope and b is the y-intercept.

Here we have 2 points (4, 51in) and (5, 57 in), then the slope is:

a = (57 in - 51 in)/(5 - 4) = 6in

Then the line is something like:

L = 6in*x + b

To find the value of b, we use one of the given points, like (4, 51 in), it means that when x = 4, we must have L = 51in.

51in = 6in*4 + b

51in = 24in + b

51in - 24 in = b = 27in

Then the linear equation is:

L = 6in*x + 27in

The length for a total of 21 carts is what we get when we evaluate in x = 21, so we will get:

L = 6in*21 + 27in = 153 in

If you want to learn more about linear equations:

https://brainly.com/question/4025726

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