Study Guide 1-10
Jen bought 4 gourmet cupcakes for $13. What equation can be used to model the total cost, y, for x cupcakes?
How much money does she need to buy 12 cupcakes?
y = $3.25x
$3.25 x 12 = $39.00
She needs $39.00 to buy 12 cupcakes.
Hans has two coupons for shoes. Coupon A: $22 rebate on $63 shoes. Coupon B: 30% off of $63 shoes.
Find the price of the shoes using each coupon. Which coupon gives the lower price?
Coupon A (rebate):
Coupon B (discount):
Price Comparison:
Result:
Coupon A (rebate):
Price without rebate: $$63.00
Rebate amount: $$22.00
Final price with rebate: $$63.00 - $22.00 = $41.00**
Coupon B (discount):
Discount rate: 30%
Price before discount: $$63.00
Discount amount: $$63.00 * (30/100) = $18.90**
Final price with discount: $$63.00 - $18.90 = $44.10**
Price Comparison:
Coupon A: $$41.00**
Coupon B: $$44.10**
Result:
Using Coupon A (rebate) results in a lower price of $$41.00** for the shoes compared to Coupon B's price of $$44.10**.
Evaluate 2x-a if a= -4/15 and x= -3/10
-2/30 or -1/15
Let's evaluate the expression 2x-a substituting a = -4/15 and x = -3/10:
Substitute the values of a and x: 2 * (-3/10) - (-4/15)
Simplify the expression: -6/10 + 4/15
Find a common denominator for the fractions:
Evaluate the fractions: -18/30 + 16/30
Combine like terms: (-18 + 16) / 30
Simplify the result: -2 / 30
Therefore, when a = -4/15 and x = -3/10, the expression 2x-a evaluates to -2/30. The expression can also be simplified to -1/15.
A construction company can remove 1/3 metric tons of dirt from a construction site in 1/6 hours. What is the unit rate in metric tons per hour? Write your answer in simplest form.
Unit rate is 1/3 metric tons to 1/6 hours
Therefore, the rate in simplest form is 2:1 metric tons per hour. This means the company removes dirt at a rate of 2 metric tons per hour.
Evaluate the expression:
-c + 7x when c=2 and x= -2
-16
-c + 7x
Substitute:
= - (2) + 7(-2)
Evaluate:
= -2 - 14
Combine like terms:
= -16
Therefore, when c=2 and x=-2, the expression -c + 7x evaluates to -16.
simplify the expression 2(5x-1) + 4x-(7x-10)
7x+8
We can simplify the expression by distributing the terms, combining like terms, and removing parentheses.
Steps to solve:1. Distribute the terms:10x−2+4x−(7x−10)
2. Distribute the terms:10x−2+4x−7x+10
3. Combine like terms:10x+4x−7x−2+10
4. Combine like terms:7x+8
Answer:7x+8
Solve the following proportion for y. Round your answer to the nearest tenth.
17/7 = y/4
1. cross multiply to get 68=7y
2. divide both sides by 7 to isolate and find the value of y. This gives you 9.714=y
3. rounded to the nearest tenth give you 9.7
Compute:
4.32-12.751=
6.72+ -4.38=
-8.431
2.34
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The price of an item yesterday was $130. Today, the price rose to $221. Find the percent increase.
70% increase.
Percent increase = (Price difference / Yesterday's price) * 100 = ($91 / $130) * 100 = 70.00%
Liz is shopping for a new video game system. Here are the regular price of the game system at several stores.
Store A $289
Store B $309
Store C $309
Each store is having a sale. Where should Liz purchase her game for the best deal?
Store A 15% off original price
Store B with membership of the reward program receive 30% off the original price of a game. She needs to become a member at a cost of $29.99
Store C 50% off of all game systems priced over $250
Store C is the best deal.
Store A $245.65
Store B $216.30 with the discount, plus $29.99, which is $246.29
Store C $154.50
23525 divided by .25
94,100
A TV has a listed price of $508.95 before tax. If the sales tax is 7.25%, find the total cost of the TV with sales tax included. Round your answer to the nearest cent, as necessary.
Tax is $36.898875 (rounded would be $36.90)
$508.95 plus $36.90 = $545.85
To simplify the expression -14 + 73 + 27 + (-11) Corey began by rewriting it as (73+27) + (-14 +(-11)). Which properties did Corey use to rewrite the expression?
Corey used the commutative property of addition to rewrite the expression.
The commutative property states that the order in which you add numbers does not affect the sum. In other words, for any numbers a, b, and c:
a + b = b + a
In this case, Corey grouped the positive terms (73 and 27) and the negative terms (-14 and -11) separately. Since the order of addition doesn't matter, as long as you add the same numbers together, the sum will remain the same.
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