Creating Equations for Situations
What equation can be used to help create other equations representing different situations/relationships between two quantities that have a proportional relationship?
y = kx
How do you take the percentage of something using a calculator? Give an example.
Percentage must be put into decimal or fraction form then multiplied by amount we want to find the percentage of. Ex. 0.25 x 100 = 25, .11 x 1000 = 110, 0.025 x 700 = 17.50
During the first semester Carlos' grade average was 80. He set a goal to raise his average to 84 for the second semester. For this situation, how can you identify the percentage that carlos needs to raise his grade?
84 / 80 = 1.05 (Amount additional to 1 is the percent increase needed.)
Take answer and subtract 1 to get what percentage carlos' first semester grade needs to increase by.
The cable television company reduced rates 20% last year. If the original service cost $20.50, what is the new cost?
Multiplying 20.50 by 1 would keep it the same. Subtracting .2 from 1 represents a 20% decrease in decimal form from the original price.
1-.2 = .80 x 20.50 = 16.40 (Representing $16.40 which is 80% of the original cost that was discounted 20%)
.15 x 35 = 5.25
Ava has a recipe for chocolate chip cookies. She uses 5 cups of flour to make 3 batches of cookies. Jeriona will follow the same recipe. She will make c batches of cookies using f cups of flour. What equation represents the relationship between c and f? *************
c = 3/5f
f = 5/3c
Mark bought a new suit for $139. The sales tax was 8.5%. What is the amount of sales tax?
.085 x 139 = 11.815 (In this case we would have to round up to $11.82)
The store bought a pair of shoes for $25, and sold it for $45. What percentage was the markup? *******
45/25 = 1.8 ... 1.8 - 1 = .8 (Which represents 80%)
With a coupon, you can get a pair of shoes that normally costs $84 for only $72. What percentage was the discount?
To find the discount percentage here you want to, again, put the new price over the original. Which is 72/84. 72/84 = 0.857 but this is not the discount percentage. It is the percentage 72 is of the original.
.857 - 1 will give you the discount, which is -0.143. So the discount was 14.3%
A circular track is ½ mile long. Jonah runs on this track, completing each lap in 1⁄16 of an hour.What is Jonah’s running speed? Include the unit of measure. ************
1/2 x 16 = 8 miles per hour
When filling a mop bucket, the amount of water required varies directly with the amount of detergent. If 50 ml of detergent requires 4 liters of water, what is an equation that can represent this relationship?
d= detergent
w= water
w = 4/50d
The Washington family had dinner at a restaurant, and the bill was $85.00. They gave their server a $13.60 tip. What percent of the cost of the meal did they leave as a tip?
13.60 / 85.00 = 0.16 (Which represents 16%)
A pair of designer sneakers was purchased for $120. Since they were purchased, their price has increased by 15%. What is the new price?
120 x 1.15 = 138 (representing $138 in this situation)
Multiplying 120 by 1 would keep the price the same, adding .15 to 1 represents a 15% increase for something... We then multiply 1.15 x 120 to find our answer.
If the regular price of an item is x dollars, what is the discount price in dollars after a 20% discount?******
1 x original price will give us an equal price/one that is the same. 1 - .20 represents that original price minus 20% in decimal form. 1 - .20 = 0.80 which is the percentage of the original price that is to be paid.
Now we take 0.80 x(of) X to represent the price in dollars after a 20% discount.
Stephanie saw in an ad in the paper that her favorite kind of perfume was on sale for 25% off.
If the sale price was $15, what was the original price of the perfume?
15 / .75 = 20 in this case it could be solved using a double number line diagram as well.
A taco recipe serves 8. It uses 2 pounds of
ground beef. What is an equation that can represent this relationship between the servings and pounds of ground beef?
s= serving
p=pounds
p= 1/4s
A car salesman earns a 1.5% commission on every car he sells. What is his commission for selling a car for $7500? ********
0.015 x 7500 = 112.50 (Which in this situation represents $112.50)
A car is 140 inches long. A truck is 75% longer than the car. How long is the truck? ************
1.75 x 140 = 245 inches
1.75 represents 1 and 75% more (in decimal form) of the original length (the car)
Today, everything at the store is on sale. The store offers a 20% discount.
The regular price of a T-shirt is $18. What is the discount price?*****
1 - .20 (20% in decimal form) = 0.80 (percentage of original price to be paid..)
.80 x(of) 18 (original price) = 14.40 ("discount price")
Jewel is paying for a $40 meal. She has a 20%-off coupon for the meal. After the discount, a 7% sales tax is applied. What does Jewel pay for the meal? *********
40 x 0.80 = 32 (dollars to pay after discount)
32 x 1.07 = 34.24 (Total including 7% tax on the discounted price)
When rice is cooked, the amount of water required varies directly with the amount of rice. If 2 cups of rice requires 4.5 cups of water, What is an equation that can represent this relationship?
r=cups of rice
w= cups of water
w=4.5/2r
Carol had a birthday party at a local pizza restaurant. The bill came to $54.80, not including the tip. If she wants the tip to be 15%, how much would that add to the bill?
.15 x 54.80 = 8.22 (In this case, that means $8.22 would be added to the bill.)
The water level in a reservoir is now 52 meters. If this was a 23% increase, what was the initial depth?
i=initial depth
1.23i = 52
i = 52 / 1.23 = 42.28
Could also use double number line diagram...
Today, everything at a store is on sale. The store offers a 20% discount.
The discount price of a hat is $22. What is the regular price?***********
22 / 0.80 = 27.50
The price of gold is often reported per ounce. At the end of 2005, this price was $513. At the end of 2015, it was $1060. By what percentage did the price per ounce of gold increase?
Our new price will be over the old price to find the percent increase.
1060/513 = 2.066 - 1 = 1.066 (100% + 6.6%)
if the new price was 513 it would be 513/513 equaling 1, therefore the amount added to 1 is the increase.