(a) Let x be the variable. The variable will stand for the number of additional minutes used (in addition to the minutes built into the default plan). For example, if x = 10, then Allegra used 10 additional minutes on top of what her plan allows. If x = 0, then Allegra simply pays the $65 without any extra charge.
(b) The equation is 0.10x+65 = 73.40; the 65 represents the fixed cost of 65 dollars per month regardless of how many additional minutes you use. Then you add on 0.10x on top of that to get the total 0.10x+65, which is set equal to 73.40 as this is the given bill for this particular month.
(c) Solve the equation from part (b) to get... 0.10x+65 = 73.40 0.10x+65-65 = 73.40-65 0.10x = 8.40 0.10x/0.10 = 8.40/0.10 x = 84
(d) Allegra used 84 additional minutes as this is the solution to the equation mentioned in part (b) and solved in part (c). To check the answer, simply replace x with that value 0.10x+65 = 73.40 0.10x*84+65 = 73.40 8.4+65 = 73.40 73.40 = 73.40 The answer checks out
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Problem 2
P = principal (amount deposited) i = interest only r = interest rate in decimal form t = time in years
We are given the following: i = 2800 r = 0.04 (decimal version of 4%) t = 3.5 and we want to solve for P
i = P*r*t 2800 = P*0.04*3.5 2800 = P*0.14 2800 = 0.14P 2800/0.14 = 0.14P/0.14 20000 = P P = 20000
Andrea should deposit $20,000 into the account (to earn $2,800 after 3.5 years; where the interest rate is 4%)
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Problem 3
|4x-8| - 3x = 6x+2 |4x-8| - 3x+3x = 6x+2+3x |4x-8| = 9x+2 4x-8 = 9x+2 or 4x-8 = -(9x+2) 4x-8 = 9x+2 or 4x-8 = -9x-2 9x-4x = -8-2 or 9x+4x = -2+8 5x = -10 or 13x = 6 x = -10/5 or x = 6/13 x = -2 or x = 6/13
The two possible solutions are: x = -2 or x = 6/13
However, x = -2 does not work since |4x-8| - 3x = 6x+2 |4(-2)-8| - 3(-2) = 6(-2)+2 |-8-8| + 6 = -12+2 |-16| + 6 = -10 16 + 6 = -10 22 = -10 which is false
Luckily, x = 6/13 does work and I'll leave that as an exercise to have you check it.