Question

To make pancakes, 2 cups of batter r used to make 5 pancakes, 6 cups of batter r used to make 15 pancakes, & 8 cups of batter r used to make 20 pancakes. PART 1 [Part 2 below]?

PART 2! Show that the relationship between the number of cups of batter and the number of pancakes is a proportional relationship. Then write an equation for the relationship.

Answer 1

number of pancakes`= 2.5 xx` number of cups of batter

Explanation:

`(5" pancakes")/(2" cups of batter")rarr (2.5 " pancakes")/("cup")`

`(15" pancakes")/(6" cups of batter")rarr (2.5 " pancakes")/("cup")`

`(20" pancakes")/("8 cups of batter")rarr (2.5 " pancakes")/("cup")`

Note that the ratio of `"pancakes":"cups"` remains a constant so we have a (direct) proportional relationship.

That relationship is
`color(white)("XXX")p=2.5 xx c`
where `p` is the number of pancakes and `c` is the number of cups of batter.

Answer 2

Relationship equation between number of pancakes and cups of batter required is `p=2.5*b`

Explanation:

Let `b` represents cups of batter and `p` represents number of

pancakes. `p prop b or p= k*b or k = p/b ; k` is constant of

proportionality. `p= 5 , b=2 :.k= p/b=5/2=2.5`

`:. p=2.5*b` is the relationship between `p and b`.

It holds good also when `p= 15 , b=6 :.k= p/b=15/6=2.5`

and for `p= 20 , b=8 :.k= p/b=20/8=2.5`. Therefore

relationship equation between number of pancakes and cups of

batter required is `p=2.5*b` [Ans]