Ratio word problems

[Amarianna]

Hello can you please help me with this the ratio of blueberries to strawberries is 5.7 if there are 21 strawberries how many blueberries are there can you please help me to put this into a format I’m a little lost

 

[Steven G]

5:7 which really means 5 blueberries: 7 strawberries or 5 blueberries to 7 strawberries.

Imagine that there are packages in the grocery store that has exactly 5 blueberries and 7 strawberries. Now you need to have 21 strawberries. So how many of these packages must you buy to have 21 strawberries? Now how many blueberries will you have? That will be your answer!

Alternatively you can figure out what to multiply 7 by to get 21. Then multiply this number by 5 and that will be your answer. That is you can multiply both 5 and 7 by any number (except 0) and the ration will remain the same.

 

[Otis]

… the ratio of blueberries to strawberries is 5.7 …

Hi Amarianna. When I first saw 5.7, I'd thought it was five and seven-tenths, heh. There are three ways to express a ratio -- using the word 'to', using a colon, or using fraction form. Because you'd used the word to between "blueberries" and "strawberries", you should use the same form on the other side and write "5 to 7". Here are the three ways, written out.

blueberries to strawberries is 5 to 7

blueberries : strawberries is 5 : 7

blueberries/strawberries = 5/7

When two ratios are equal, we call that a proportion. In your exercise, you need to determine the number of blueberries (i.e., numerator in the lefthand ratio, below) when the number of strawberries is 21 (denominator of that ratio).

\(\displaystyle \frac{?}{21} = \frac{5}{7}\)

When we know three of the four numbers in a proportion, we can find the missing number using this method: Multiply numbers on the diagonal, then Divide by the number not used.

Here's an example, using a simple trail snack recipe. Mix 2 parts M&Ms with 5.5 parts Peanuts. In other words,

M&Ms : Peanuts is 2 : 5.5

We're told that 49.5 scoops of Peanuts makes enough snack for a hiking group. How many scoops of M&Ms will we need?

Write the ratios in fraction form, using the known number of peanut scoops.

\(\displaystyle \frac{?}{49.5} = \frac{2}{5.5}\)

To find the unknown number above, we multiply on the diagonal and divide by the number not used. The "diagonal" is an imaginary line drawn through the numerator on one side and the denominator on the other side (or vice versa). Above, we see the numbers 49.5 and 2 on the diagonal, so we multiply them. Then, 5.5 becomes the number not (yet) used, so we divide by it.

49.5 × 2 ÷ 5.5 = 18

We'll need 18 scoops of M&Ms.

Jomo has described another approach to solving a proportion that is similar to how we think when working with common denominators. You may already know that adding fractions like 2/3+7/12 requires converting 2/3 to obtain a common denominator (in this case, 12). How many twelfths is 2/3?

\(\displaystyle \frac{2}{3} = \frac{?}{12}\)

We work it out by asking ourselves what number we need to multiply 3 by to get the common denominator 12. That number is 4, so we multiply 2/3 by 4/4.

\(\displaystyle \frac{2}{3} × \frac{4}{4} = \frac{8}{12}\)

With simple proportions, we can reason the same way when one of the four numbers is missing. So, here's an example for what Jomo has in mind.

An experiment requires two girls for every three boys, in a group. If the group has 12 boys, how many girls are needed in the group? We write the proportion.

\(\displaystyle \frac{?}{12} = \frac{2}{3}\)

What number do we multiply 3 by, to get 12? That's 4. So we also multiply the 2 on top by 4, and that gives us the missing number 8.

Jomo's approach is good for students who've memorized the multiplication table and the numbers in the proportion are smaller, whole numbers. The calculation that I first described (multiply on the diagonal and divide by the number not used) can be easier when we have other numbers -- like the 5.5 and 49.5 in that first example.

Hope that helps. You can see more information about ratios on this page and more examples with proportions on this page. Let us know, if you still have questions. Please show any work that you tried.

?

 

[Deleted member 4993]

Hello can you please help me with this the ratio of blueberries to strawberries is 5.7 if there are 21 strawberries how many blueberries are there can you please help me to put this into a format I’m a little lost

How many piles of 7 strawberries can you make out of 21 strawberries?

3

Now make 3 piles of blueberries with 5 blueberries in each pile.

How many blueberries would you need in total?

Continue.......

 

[Otis]

I ate all the blueberries, ha! (That's why I'm purple.)

 

[Steven G]

I ate all the blueberries, ha! (That's why I'm purple.)

OK, fine. Can you tell me how many you ate?