Solve the problem using proportion and variation. Show solution please Thank you!☺️

Question

A recipe for guacamole dip calls for 5 avocados. If they advertised at 3 for $1.98, what will 5 avocados cost?

Answer 1

first, find the unit price ($1.98 / 3), then multiply that price for one by five!

Answer 2

This is a typical proportion problem presented in either Pre-Algebra or Algebra. While I short-cut may work, you are best served understanding the reason and manner in which to set up a proportional equation. 

What you want to remember is to establish a proportion equation premised on the information you are provided in the problem. Often, with word problems you will find additional unnecessary information. This should not hinder you, however, in resolving the problem. 

In the problem above you are told "A recipe for guacamole dip calls for 5 avocados." This is irrelevant information for this particular problem and is an example of what I was referencing above regarding extra information added to word problems. What if a particular recipe called for 20 avocados? It matters little what the recipe calls for because you are wanting to know with certainty how much 5 avocados would cost given the pricing information you have in the problem. 

However, what you DO need to know is that avocados are being advertised at a price of 3 for $1.98. 

Therefore, the first part of your proportion should be set with the number of avocados being the numerator of a fraction with the price being the denominator. 

Therefore, the proportion equation would begin looking like this: 

3/1.98  

Then, you will notice the next information provided or not provided in the problem is the cost of 5 avocados. 

Therefore, the second fraction is set up as follows: Since you do not know the cost or price of 5 avocados, your second fraction will have an x in the denominator. Why? Because over in the first fraction of your proportional equation your price is in the denominator, correct? 

However, you DO know the number of avocados involved in that second fraction, don't you? The answer is obviously 5. You are given that information.

Therefore, your second fraction of this proportional equation will be as follows: 

5/x 

Now that you have the two sides of your equation, you can determine the missing variable (in this case x or the cost of five avocados). 

Therefore, the following equation emerges: 

3/1.98 = 5/x   THIS is the proportional equation. 

Now you need to solve this equation for x. 

If you cross-multiply your fractions on either side of the equal sign you will arrive at the following: 

3x (this is the numerator from the left fraction and denominator from the right fraction) is equal to 1.98 (5) the denominator of the left fraction times the numerator from the right fraction. 

Therefore, your next step will look like this: 

3x = 1.98(5) 

Now solve for x 

First, multiply the 1.98 times 5 on the right side of your equation. Your answer should be: 9.9

That means your equation now looks like this: 

3x = 9.9 

Now you must solve for x to arrive at your answer. 

To do so, you need to divide 3 into 9.9 to leave x to itself. Doing so leaves you with the answer of 3.3

Therefore, the answer is 3.3. You can automatically add a zero to the end of this answer and you have a final answer of 3.30 meaning it will cost you $3.30 to purchase the 5 avocados.