A recipe calls for 3 cups of flour to make 2 batches of dinner rolls. One batch makes 15 rolls. Laura is making dinner for 12 people and only needs one roll per person. What proportion will help Laura find how much flour is needed to make 12 dinner rolls?
A. 3/30 = x/12
B. 3/2 = x/12
C. 3/15 = x/12
D. 12/15 = x/3

A

Step-by-step explanation:

3 cups of flour produces 2 batches of dinner rolls. So, if one batch makes 15 rolls, then 2 batches makes 30 rolls. Therefore, 3 cups of flour produces 30 rolls.

Laura wants to find how much flour she needs to make 12 rolls.

Here's the setup:

Let x be the number of cups of flour needed. Then,

(3 cups of flour)/(30 rolls)=(x cups of flour)/(12 rolls)

This is the set up for all equations involving ratios. The units should be consistent. Notice how I have flour/rolls=flour/rolls.

It is not necessary to solve the equation, but you should to make sure your answer makes sense. By cross-multiplying, we get x=(3*12)/30 or 1.2 cups.

This solution makes sense. Because 3 cups of flour produces 30 rolls, one cup produces 10 rolls. We need slightly more than 1 cup to get 12 rolls.

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺