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Math 70 Exam 2 Solutions
1. To find the temperature in degrees Fahrenheit, evaluate the formula with C = 30.
So, the temperature is 86°Fahrenheit.
2. (a) Distribution with the inner set of parenthesis:
So, 2y[3y + 2(y − 1)] simplifies to 10y^2 − 4y.
3. (a) Simplifying the right-side of the equation: x + 3 = −4 -> x = −7 ( Subtracting 3 from both sides)
Solution : x = −7
Left-side of equation: −7 + 3 = −4
Right-side of equation: −12 + 8 = −4 √
(b) Dividing both sides by 5:
Solution: y = 0.5
Left-side of equation: 5(0.5) = 1.5
Right-side of equation: 1.5 √
(c) Combining like terms on the left -side of the equation:
(Dividing both sides by 4 and simplifying)
Solution: x =3/2
Left-side of equation:
Right-side of equation:
(d) Distributing the left-side of the equation:
|(Subtracting 2x from each side.)|
|( Adding 8 to each side .)|
|(Dividing both sides by 2.)|
Solution: x = 5
Left-side of equation: 4(5 − 2) = 4(3) = 12
Right-side of equation: 2(5) + 2 = 10 + 2 = 12 √
(e) Here are a couple of ways to solve this :
(Subtracting 3/2 from each side.)
• Clearing the fractions:
|x = −3||(Subtracting 9 from both sides.)|
Solution: x = −3
Left-side of equation:
Right-side of equation: 1 √
4. Unknowns :
Pounds of peanuts = x
Pounds of chocolate = 3x
Equation: Since we want a total of 20 pounds when
we combing peanuts and chocolate, the
equation is x + 3x = 20.
Combining the like-terms on the left side:
|4x = 20|
|x = 5||(Dividing both sides by 4.)|
-> You need 5 pounds of peanuts and 15 pounds of chocolate.
5. Using the equation Distance = Rate(Time), we have that
Distance = (1.4 ft/min)(20 min) = 28 feet.
So, Sam will travel 28 feet in 20 minutes.
No matter how you tip, you will have to pay the $40 for
the dinner and $40(0.10) = $4 for the tax,
which would give you a total of $44 not including the tip.
If you apply the tip to just the bill without tax, then
you are tipping on the amount of $40. So, you
would give a tip of $40(0.15) = $6.
If you apply the tip to the bill including tax, then you
are tipping on the amount of $44. So, you would
give a tip of $44(0.15) = $6.60.
So, if you tip on the pre -tax amount, you leave a tip of
$6. If you tip on the post-tax amount, you leave
a tip of $6.60.
Answer: The difference is $0.60.