........?.............-89
4:14 , 6:21, 8:28, 10:35!!!
Write and solve an equation of ratios:
5 65
--- = ------
4 x
Then 5x = 260, or x = 52. There are 52 girls on the team. Note, as a check, that 65/52 reduces to 5/4, as it must.
When we say two quantities 
and 
are proportional to one another, there are two ways we could mean this.
- If is *directly* proportional to , then we mean that as changes, changes in the same direction. In other words, if is in/decreased, then also in/decreases. The rate of in/decrease doesn't have to be one-to-one; for example, we could have increase by 1 unit while would proportionally increase by 5 units. In this case, we'd have 
.
- On the other hand, if is *inversely* proportional to , then a change in results in a change in that goes in the opposite direction. A common example involves taking a rectangle of constant area and adjusting the width and length . If the rectangle has an area of 5 square units, then we could have 
and 
, or we could have 
and 
, or 
and 
, or any combination of and such that 
is satisfied.
In both cases, we call 5 the "constant of proportionality".
On to your exercises:
(1a) Looks like 
stands for number of apples. Then we're told that the cost 
, which means that for every apple, the cost increases by 2.3 dollars. So the constant of proportionality is 2.3. In the language of proportionality, we could then say that the cost of apples is directly proportional to the number of apples by a factor of 2.3.
(1b) 5.4
(1c) 12.5
the answer is 3. 3 is the greatest common factor
