At a bakery there are 45 different kinds of breads and sweets. If the ratio of sweets to breads is 4:5, how many types of breads are there?

Question

At a bakery there are 45 different kinds of breads and sweets. If the ratio of sweets to breads is 4:5, how many types of breads are there?

Answer 1

4 bread to 5 sweets = ratio. the total of that ratio added is 9 breads and sweets. the actual number of breads and sweets is 45. to get from the total ratio of 9 to the actual number of 45 we times 9 by 5.  ratio times 5 = actual number

   4:5 x 5 = 20:25   20+25=45   20 breads and 25 sweets

Answer 2

you can also do it with one variable, since you already know the ratio and the sum:

 

4x + 5x = 45

9x = 45

x = 5, so in the 4:5 ratio, you get 20:25, with 25 being the number of breads.

 

Mmmm.... sweets and breads.... :-)

 

Matt in NY

Answer 3

Let's say the number of sweets is 's' and the number of breads is 'b'.

 

We know the total is 45, so the first equation is " s + b = 45 "

 

We also know that the ration of sweets to breads is 4:5, so the second equation is " s/b = 4/5 "

 

We want to find out how many types of breads there are, so we will solve for "b". 

 

1. The first step is to get rid of "s" in one of the equations, by replacing it with an expression for "s" from the other equation.

• Let's find an expression for s from the first equation: " s + b = 45 ".  Subtracting "b" from both sides of the equation yields the new equation: " s = 45 - b ".
• Now, we can replace the "s" in the second equation with the expression "45 - b" (since they are equivalent, according to the first equation).  So the second equation: " s / b = 4 / 5 " becomes: " (45 - b) / b = 4 / 5 "

2. The second step is to solve the new version of the second equation for "b".

• Let's multiply both sides of the equation by 5 to get rid of the fraction on the right side of the equation:

5 x (45 - b) / b = 4

• Using distribution, multiply the 5 across the "(45 - b)":

(225 - 5 x b) / b = 4

• If  "b" is not equal to 0, (*) then we can multiply both sides of the equation by "b" to get rid of the fraction on the left side of the equation:

225 - 5 x b = 4 x b

(*) NOTE: It's important to check at the end that "b" is not equal to 0, otherwise what we just did is not legal

• Add "5 x b" to both sides:

225 = (4 x b) + (5 x b)

• which can be simplified to:

225 = (4 + 5) x b   

          or:

225 = 9 x b

• divide both sides by 9 to get the value of "b":

225 / 9 = (9/9) x b = b

          or:

25 = b  [this is the answer]

 

3. Check your work:

• b = 25, and " s = 45 - b " (modified first equation from above), so s = 45 - 25 = 20
• verify second equation: " s/b = 4/5 ".  Does  "20/25 = 4/5"? 

Remember, 20=4x5, and 25=5x5, so 20/25 could be written as "(4x5)/(5x5)"

You can divide the top and the bottom of the fraction by the same number (5) and the fraction will remain the same ratio, so you get 4/5.   The answer above ( b = 25 ) is correct. :-)