Writing Linear Functions

In (a) part write at expression and for (b) part write an equation
• (a)6 greater than a number. x + 6
• (b)6 is greater than a number. 6 > x

The product of 6 and a number, decreased by 12
• We have the product of 6 and a number, write this as 6x
• The product is decreased by 12, write this as 6x - 12

The quotient of three times a number and 7
• Three times a number, or 3x will be the numerator
• Since we have a quotient we must have division, in this case by 7
• (3x/7)

The sum of a number and -4 is 12. Find the number
• First, the sum of a number and -4 can be written as x + (-4)
• That sum equals 12, x + (-4) = 12 , this is the equation we were asked to find
• Solving for x we have x = 12 + 4
• x = 16 , this is the value of x

We are to find the profits of each corporation
• GM + GE profits totalled $13.5 billion, GM + GE = 13.5
• GE profits were$0.3 billion less than GM, GE = GM - 0.3
• Substituting we have GM + (GM - 0.3) = 13.5
• 2 GM = 13.8
• GM =$6.9 billion
• GE = 6.9 - 0.3 = $6.6 billion

Melissa won $60,000 and put it into two investments.
• One investment earned 2%, let us say she put x dollars into that investment
• The other investment earned 3%, she put 60,000 - x dollars into this investment
• From the two investments she earned a total of $1,600
• Let's put this information into a table

• Rate	Amount	Interest
  0.02	x	0.02x
  0.03	60000 - x	0.03(60000 - x)
  Totals	60000	1600

• We have 0.02x + 0.03(60000 - x) = 1600
• 0.02x + 1800 - 0.03x = 1600
• -0.01x = - 200
• x = $20,000 at 2%
• 60000 - x = $40,000 at 3%

How much red dye do we add to 4 gal of a 25% dye solution to get a 40% solution?
• We have 4 gal of 0.25 dye (25%)
• We will add x of 1.00 (100% or pure dye)
• Putting our data into a table it looks like this

• Concentration	Amount	Amount of Dye
  0.25	4 gal	0.25(4)
  1.00	x	x
  0.40	4 + x	0.4(4 + x)

• We know that 0.25(4) + 1x = 0.4 (4 + x)
• 1 + x = 1.6 + 0.4x
• x - 0.4x = 1.6 -1
• 0.6x = 0.6
• x = 1 gallon , we must add 1 gallon of pure dye