Question

A recipe that makes 8 jumbo blueberry muffins calls for 1 3/4 teaspoons of baking powder. How much baking powder is needed to make 5 dozen jumbo muffins?

Answer 1

It takes
`13(1)/(8)` teaspoons of baking powder to make 5 dozen jumbo muffins.

Explanation:

Two quantities a and b are directly proportional if when multiplying or dividing one of them by a number, the other is multiplied or divided by that number. That is, if one magnitude grows, the other will grow in the same proportion; while if one magnitude decreases, the other will decrease in the same proportion.

The simple rule of three allows us to establish the relationship of proportionality between two known values ​​and, based on the knowledge of a third quantity, to calculate the value of the fourth.

In other words, it is necessary to know two magnitudes that will be proportional to each other, and a third magnitude, from which you want to find out, will be a fourth term through the relationship:

a ⇒ b

c ⇒ x

Then:
`x=(c*b)/(a)`

where a, b, and c are the known data, and x is the fourth unknown.

In this case, the rule of three can be applied as follows: if 1 dozen contains 12 muffins, 5 dozen jumbo muffins, how many muffins does it contain?

`amount of jumbo muffins=(5 dozen*12 jumbo muffins)/(1 dozen)`

amount of jumbo muffins= 60

Now you apply the following rule of three: if 8 jumbo blueberry muffins requires 1 3/4 ( or, which is the same, 7/4)teaspoons of baking powder, 60 jumbo muffins how many teaspoons of baking powder does it require?

`teaspoons of baking powder=(60*(7)/(4) )/(8)`

teaspoons of baking powder=
`(105)/(8)` =
`13(1)/(8)`

It takes
`13(1)/(8)` teaspoons of baking powder to make 5 dozen jumbo muffins.