------------------------------------------------------------------------------------------------- Assumptions ------------------------------------------------------------------------------------------------- Let x be the amount of 25% orange juice Let y be the amount of 10% orange juice
------------------------------------------------------------------------------------------------- There are 15 litres of 13% orange juice ------------------------------------------------------------------------------------------------- x + y = 15
------------------------------------------------------------------------------------------------- The 15 litres of juice is 13% orange juice ------------------------------------------------------------------------------------------------- 0.25x + 0.1y = 15 x 0.13 0.25x + 0.1y = 1.95
------------------------------------------------------------------------------------------------- Rewrite the equations and solve for x and y ------------------------------------------------------------------------------------------------- x + y = 15 ----------------------- (Equation 1) 0.25x + 0.1y = 1.95 ----------- (Equation 2)
(Equation 1): x + y = 15 x = 15 - y ----------- (Substitute into Equation 2)
------------------------------------------------------------------------------------------------- Answer: 3 liters of 25% of orange juice with 12 liters of 10% orange juice -------------------------------------------------------------------------------------------------
Multiplication of positive and negative integers is related to multiplication with positive and negative fractions through the multiplication rule for integers. If you multiply a two fractions with same signs, they would result in positive; in the other hand, if you multiply two signs with different sign, it would result to a negative integer.
Division is the usual shortcut for repeated subtraction. You could subtract 5.5 from 264 until you get to zero. You would have to do 48 subtractions. It is easier to divide 264 by 5.5 to see how many times it goes.
