Question

For each of the problems below, do the following:

(a) Identify the unknown quantity (quantities)
(b) Define a variable (or variables) to represent the unknown
(c) Write an equation that describes the information given in the statement of the problem
(d) Solve the equation and answer the problem.
3. You have a 4 litre jug of 3.5% milk (milk that contains 3.5% fat). How much skim milk (0% fat) do you need to add to it to obtain milk which will have 2% fat?
4. 280 people joined the community band. Some intended to play a woodwind instrument, some a brass instrument, and the others percussion. If 2 times as many people were planning to play a woodwind instrument as a brass instrument, and if 80 fewer were going to play percussion than a brass instrument, how many people were planning to play each type of instrument?

Answer 1

Answer: (3) 3 liters (4) Woodwind = 180, Brass = 90, Percussion = 10

Explanation:

3) Set up a table. Multiply across and add down to create the equation.

`\begin{array}l&\underline{\quad Qty\quad}&\underline{\quad \% \quad}&\underline{\quad Qty * \% \quad}\\\text{Whole Milk}&4&.035&4(.035)\\\underline{\text{Skim Milk\quad}}&\underline{\qquad x\qquad} &\underline{\qquad 0\qquad}&\underline{\qquad x(0)\qquad}\\\text{Mixture}&4+x&.02&4(.035)+x(0)\\\end{array}\\\\\\.\qquad \qquad (4+x)(.02)=4(.035)+x(0)\\\\.\qquad \qquad (4+x)(.02)=.14\\\\.\qquad \qquad 4+x\quad \qquad =7\qquad \longrightarrow \text{divided both sides by .02}\\`

x = 3 ---> subtracted 4 from both sides

4)

Woodwind: 2x

Brass: x

Percussion: x - 80

TOTAL: 4x - 80 = 280

4x = 360 ----> added 80 to both sides

x = 90 ---> divided 4 from both sides

Woodwind: 2x ---> 2(90) = 180

Brass: x ---> 90

Percussion: x - 80 ---> 90 - 80 = 10