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Alex17521
1 day ago
11

How do you write algebraic expressions to model quantities

Mathematics
2 answers:
AnnZ [9K]1 day ago
7 0
The correct answer is:

We pick a variable to stand for the unknown. Then we search for key words that indicate which operations are being used. For instance, the word "sum" signals addition, "product" denotes multiplication, "difference" means subtraction, and "quotient" refers to division. The word "Is" corresponds to equals. We make sure to preserve the order items appear in the problem so the algebra matches the wording.

For example:

Two more than 3 times a number is 23.

Let the unknown be x.
Three times the number is 3*x = 3x.
Adding two to that yields 3x+2.
That expression "is" 23, so we set it equal to 23: 3x+2=23.
Zina [9.1K]1 day ago
3 0
To create algebraic expressions that represent quantities, translate the verbal description into mathematical terms following the sentence’s structure. For example, “one minus a number equals zero” becomes
1. 1 – n = 0.
Another example: John bought 25 apples and Julia bought 15. If Niccole bought twice as many as Julia, how many apples did Niccole buy?<span><span>
Steps:</span>First, restate the situation clearly so you can identify the relationship and how to form the expression.</span> <span><span>
Solution:</span>Julia = 15 apples Niccole = 2Julia </span>Thus, 2Julia = 2(15) = 30 apples.




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You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). O
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3 days ago
Sarah can bicycle a loop around the north part of Lake Washington in 2 hours and 30 minutes. If she could increase her average s
Leona [9271]

Response:

The loop's length is roughly 49.58 km.

Step-by-step details:

Given:

Duration to cycle the loop = 2 hours and 30 minutes

It is known that;

60 minutes = 1 hour

30 minutes = 0.5 hour

therefore, 2 hours and 30 minutes = 2+0.5 = 2.5\ hrs

∴ Time to cycle the loop = 2.5 hours

Let 's' denote the cycling speed.

Denote the total loop distance as 'd'

From our understanding;

Distance equals speed times time.

Representing this as an equation we have;

d =2.5s \ \ \ \ equation \ 1

Given:

If her speed increased by 1 km/hr, the time taken around the loop would decrease by 7 minutes.

As a result, we can say;

Speed =s+1

The time then will be shortened by 7 minutes.

7 minutes = 0.12 hours

Consequently, time = 2.5 - 0.12 = 2.38

Again, Distance is calculated as speed times time.

This can be expressed with equations;

d =2.38(s+1) \ \ \ \ equation \ 2

The distances are equivalent in both scenarios, thus we will determine speed by equating the equations.

2.5s = 2.38(s+1)\\\\2.5s=2.38s+2.38\\\\2.5s-2.38s =2.38\\\\0.12s= 2.38\\\\s =\frac{2.38}{0.12} \approx 19.83\ km/hr

So, Speed = 19.83 km/hr

Loop length (d) = 19.83\times 2.5 = 49.58 \ km

Therefore, the loop length is approximately 49.58 km.

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