These problems can be solved by using ratios. The first one is simply a ratio of 75 to 10 which can be written as 75:10. However it needs to be reduced, so it could be rewritten as 15:2, since each has a factor of 5.
The second one can be written as
Where x is the length of the scale model.
So the scale model is 9/32 feet or 3.375 inches
The 3rd problem can be expressed as
Where x is the length of the line on the map
We need to convert everything to inches, so the units match up. Multiply the denominator on the left and right by (5280*12). This converts from miles to inches.
Solve for x
Even though these numbers look nasty, they divide to get 12(there are decimal roundoffs that I forgot to put in). So the length of the line is 12 inches. This makes sense because if 1 inch is 20 miles, then 12 inches is 240 miles (12*20=240)
For the last one, the odds of choosing a green marble are the number of green marbles over the total number of marbles
# of green
P(green)= ------------
# total
6
P(green)= ------------
6+7+3
6
P(green)= ------------
16
3
P(green)= ------------
8
P(green)=3/8
So the chances of picking a green marble are 3 of 8 or a 37.5% chance
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