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Math 70 Exam 2 Solutions

1. To find the temperature in degrees Fahrenheit, evaluate the formula with C = 30.

Note:or you can simplify the numerator and denominators before
multiplying the fractions

So, the temperature is 86°Fahrenheit.

2. (a) Distribution with the inner set of parenthesis:

You can distribute the 2y into the brackets or you can combine like terms inside the brackets.
I will be combining like terms first:

So, 2y[3y + 2(y − 1)] simplifies to 10y^2 − 4y.

(b) Using the product rule for exponents :

3. (a) Simplifying the right-side of the equation: x + 3 = −4 -> x = −7 ( Subtracting 3 from both sides)

Solution : x = −7

Check:
Left-side of equation: −7 + 3 = −4
Right-side of equation: −12 + 8 = −4

(b) Dividing both sides by 5:

Solution: y = 0.5

Check:

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

Check:
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

Check:

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:

The LCD of the denominators 6 and 2 is 6. Multiplying both sides by 6:

since
x = −3 (Subtracting 9 from both sides.)

Solution: x = −3

Check:

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.

Extra Credit:

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.

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