Check Your Skills Answer Key

1. 25
   Set up a proportion:

   

   Now cross-multiply:

   
2. 35

   Set up a proportion:

   

   Now cross-multiply:

   

3. 30

   Using the Unknown Multiplier, label the number of apples 3x and the number of oranges 5x. Make a quick table:

   Apples	+	Oranges	=	Total
   3x	+	5x	=	8x

   The total is equal to 8x, and there are 48 total pieces of fruit, so:

   

   Therefore, oranges equal 5x = 5(6) = 30.

4. 48

   Using the Unknown Multiplier, label the number of nuts 5x, the number of bolts 4x, and the number of washers 6x. The total is 5x + 4x + 6x:

   

   The total number of bolts is 4(12), which is 48.

5. 

   Using the Unknown Multiplier, label the amount of flour 3x and the amount of sugar 2x. The total amount of mixture is 3x + 2x = 5x:

   

   The total amount of sugar is 2(), which equals cups.

6. 225

   Use a table to organize the different ratios:

   F : S : J
   3 : 4	3 freshmen for every 4 sophomores
   5 : 4	5 sophomores for every 4 juniors

   Sophomores appear in both ratios, as 4 in the first and 5 in the second. The lowest common denominator of 4 and 5 is 20. Multiply the ratios accordingly:

   F : S : J		F : S : J
   3 : 4	Multiply by 5	15 : 20
   5 : 4	Multiply by 4	20 : 16

   The final ratio is F : S : J = 15 : 20 : 16. There are 240 juniors. Use a ratio to solve for the number of freshmen: