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pq = 7x, qr = x + 1, and pr = 9, what is qr PQ + QR = PR 7x + x + 1 = 9 Using our equation solver, we get: x = 1 Plug in x = 1 to QR: 1 + 1 = 2

If you have 65$, how many pots can you buy, the pots are 3x + 10 Set 3x + 10 = 65 and solve for x: 3x + 10 = 65 Plugging this into our equation calculator, we get: x = 18.33

If Distance equals Speed times Time (D = S x T), then what does time equal in terms of speed and distance? Divide each side by S to isolate T: D/S = S x T/S Cancel the S's on the right side: T = D/S

1/2, 3, 5&1/2, 8......203 What term is the number 203? We see the following pattern: 1/2 = 2.5*1 - 2 3 = 2.5*2 - 2 5&1/2 = 2.5*3 - 2 8 = 2.5*4 - 2 We build our function f(n) = 2.5n - 2 Set 2.5n - 2 = 203 Using our equation solver, we get: n = 82

The sum of six times a number and 1 is equal to five times the number. Find the number. The phrase a number means an arbitrary variable, let's call it x. 6 times a number is written as: 6x the sum of six times a number and 1 is written as: 6x + 1 Five times the number is written as: 5x The...

if g(x) =5x + 3 and g(a) = 14, then what is the value of a? We set g(a) = 5a + 3 = 14 5a + 3 = 14 Using our equation solver, we get: a = 2.2

A suitcase contains nickels, dimes and quarters. There are 2&1/2 times as many dimes as nickels and 5 times the number of quarters as the number of nickels. If the coins have a value of $24.80, how many nickels are there in the suitcase? Setup number of coins: Number of nickels = n Number of...

The phone company charges Rachel 12 cents per minute for her long distance calls. A discount company called Rachel and offered her long distance service for 1/2 cent per minute, but will charge a $46 monthly fee. How many minutes per month must Rachel talk on the phone to make the discount a...

When the side of a square is doubled in length, its area increases by 432 square inches. What is the size of the original square? Original square side length is s Area = s^2 Double the side lengths to 2s New area = (2s)^2 = 4s^2 Setup the difference relation: 4s^2 - s^2 = 432 3s^2 = 432...

Erin has 72 stamps in her stamp drawer along with a quarter, two dimes and seven pennies. She has 3 times as many 3-cent stamps as 37-cent stamps and half the number of 5-cent stamps as 37-cent stamps. The value of the stamps and coins is $8.28. How many 37-cent stamps does Erin have? Number of...

In the year 1980, Rick was twice as old as Nancy who was twice as old as Michael. In the year 1992 Ric, Nancy, and Michael ages added up to 78 years. How old was Ric in 1980? Age in 1980: Let Michael's age be m Nancy's age is 2m Rick's age is 2 * 2m = 4m Age in 1992: Michael's age = m + 12...

A barn contains cows, ducks, and a 3-legged dog named Tripod. There are twice as many cows as ducks in the barn and a total of 313 legs. How many ducks are there in the barn? Let the number of ducks be d. Duck legs = 2 * d = 2d Number of cows = 2d. Cow legs = 4 * 2d = 8d 1 dog Tripod has 3...

The sales tax on a computer was $33.60. If the sales tax rate is 7%, how much did the computer cost without tax? Let the cost of the computer be c. We have: 0.07c = 33.60 Solve for c in the equation 0.07c = 33.60 Step 1: Divide each side of the equation by 0.07 0.07c/0.07 = 33.60/0.07 c =...

Sonia visited a park in California that had redwood trees. When Sonia asked how tall a certain large redwood tree was, the ranger said that he wouldn't tell its height, but would give Sonia a clue. How tall is the redwood tree Sonia asked about? Sonia said the tree is 64 times my height. The...

Dennis was getting in shape for a marathon. The first day of the week he ran n miles. Dennis then added a mile to his run each day. By the end of the week (7 days), he had run a total of 70 miles. How many miles did Dennis run the first day? Setup distance ran for the 7 days: n n + 1 n + 2 n +...

Wendy is paid $7.50 per hour plus a bonus of $80 each week. Last week Wendy earned $312.50. How many hours did Wendy work last week? Setup the earnings equation with h hours: 7.5h + 80 = 312.50 Solve for h in the equation 7.5h + 80 = 312.50 Step 1: Group constants: We need to group our...

Matthew's cat weighs 10 pounds more than his pet hamster. His dog weighs the same as his cat. If the weight of all three pets is 35 pounds, ow much does his hamster weigh? Setup weights and relations: Hamster weight: w Cat weight: w + 10 Dog weight:w + 10 Add all the weights up: w + w + 10 +...

1/n + 3/5 = 1 Subtract 3/5 from each side where 1 = 5/5 1/n + 3/5 - 3/5 = 5/5 - 3/5 1/n = 2/5 Cross multiply: 5 * 1 = 2 * n 2n = 5 Divide each side by 2: n = 5/2 or 2.5

1/n + 2/n + 3/n + 4/n = 1 10/n = 1 Cross multiply: n * 1 = 10 n = 10

2^n = 4^(n - 3) 2^n = (2^2)^(n - 3) (2^2)^(n - 3) = 2^2(n - 3) 2^n= 2^2(n - 3) Comparing exponents, we see that: n = 2(n - 3) n = 2n - 6 Subtract n from each side: n - n = 2n - n - 6 0 = n - 6 n = 6