1. you can do 90 sit-ups in 2 minutes. your friend can do 135 sit-ups in 3 minutes. do these rates form a proportion? explain
2. the ratio of quarters to dimes in a coin collection is 5: 3. you add the same number of new quarters as dimes to the collection.
a. is the ratio of quarters to dimes still 5: 3?
b. if so, illustrate with an example. if not, give a counter-example.
3. you are 13 years old, and your cousin is 19 years old. as you grow older, is your age proportional to your cousin's age? explain your reasoning

1. The relation is proportional.

2. The ratio of quarters and to dimes will not remain 5 : 3.

3. y = 6 + x, Hence, not proportional.

Step-by-step explanation:

1. I can do 90 sit-ups in 2 minutes and my friend can do 135 sit-ups in 3 minutes.

If we consider t as the time in minutes and n as the number of sit-ups, then we can write (2,90) and (3,135) as two ordered pairs.

So, the relation between t and n will be

⇒ n = 45t

Therefore, the relation is proportional.

2. The initial ratio of quarters to dimes was 5:3. If I add the same number of quarters and dimes to it then,

a) The ratio of quarters and dimes will not still be 5 : 3.

b) Let, the number of quarters was 5 then the number of dimes was 3. {As the ratio was 5 : 3}

Now, we add 3 new quarters and 3 new dimes in the collection. then, finally, the number of quarters will be (5 + 3) = 8 and the number of dimes will become (3 + 3) = 6.

Therefore, the new ratio will become 8 : 6 = 4 : 3 which is not equal to 5 : 3.

3. I am 13 years old, and my cousin is 19 years old.

So, if my age is given by x and that of my cousin is y, then

y - x = 19 - 13

⇒ y - x = 6

⇒ y = 6 + x

This relation will continue as the year passes. So, the relation is not proportional as the relation is not like y = kx. (Answer)

the answer is y = 11.54

hope this : )