# 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.)

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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