Algebra Word Problems - Flashcard set - Algebra

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A rectangle's width is half its length and its area is 72 cm². What are the dimensions of the rectangle?

Let W = width; L = length; W = L/2; W x L = 72; The width is 6 cm and the length is 12 cm.

A sum of $200 is to be divided among A, B, and C in the ratio 3:2:5, respectively. How much does each person get?$

\text{Let } x = \text{the common share unit}; 3x + 2x + 5x = 200; A = 3x = $60, B = 2x = $40, C = 5x = $100.

Dan's annual salary is twice that of Anna's. If Dan gives $10,000 to Anna, their salaries would be equal. What are Dan and Anna's annual salaries?$

\text{Let } A = \text{Anna's salary}; D = \text{Dan's salary}; D = 2A; D - 10,000 = A + 10,000; A = $20,000, D = $40,000.

A bookshop has 4 times as many books as another shop. If 75 books were transferred from the larger to the smaller shop, each would have the same number of books. How many books does each shop have?

Let S = Small shop's books; L = Large shop's books; L = 4S; L - 75 = S + 75; Small shop has 100, Large shop has 400.

A rectangle's length is three times its width. If the perimeter is 48 cm, find the rectangle's dimensions.

Let W = width; L = length; L = 3W; Perimeter P = 2(L + W) = 48; The width is 6 cm and the length is 18 cm.

A fruit stall has 4 times as many oranges as apples. If 12 oranges are sold, the number of oranges will be double that of apples. How many apples and oranges are there?

Let A = apples; O = oranges; O = 4A; O - 12 = 2A; There are 12 apples and 48 oranges.

A theater sells children's tickets at $5 and adult tickets at$ 8. If 120 tickets in total are sold and the sales amount to $800, how many of each type of ticket were sold?$

\text{Let } C = \text{children's tickets}; A = \text{adult tickets}; C + A = 120; 5C + 8A = 800; \text{80 children's tickets and 40 adult tickets were sold.}

A garden's length is 20 meters more than its width and the area is 3200 m². Find the garden's dimensions.

\text{Let } W = \text{width}; L = \text{length}; L = W + 20; W imes L = 3200; \text{The width is 40 m and the length is 60 m.}

A pool can be filled by two pipes. The first pipe alone takes 4 hours to fill the pool, and the second pipe takes 6 hours. How long will it take for both pipes to fill the pool together?

\text{Let } T \text{ be the time together}; \frac{1}{4}T + \frac{1}{6}T = 1; T = 2.4 \text{ hours or } 2 \text{ hours and 24 minutes.}

A cyclist travels 90 km in two parts. On the first part, he travels at a speed of 10 km/h. On the second part, he travels at 15 km/h. If the total time for the whole trip is 8 hours, how long does he travel at each speed?

\text{Let } x = \text{time at 10 km/h}; \text{Let } y = \text{time at 15 km/h}; x + y = 8; 10x + 15y = 90; \text{x = 3, y = 5.}

A chemist has a 60% and a 30% solution of a chemical. How much of each solution should be mixed to create 100 liters of a 50% solution?

\text{Let } x = \text{litters of 60% solution}; \text{Let } y = \text{litters of 30% solution}; x + y = 100; 0.6x + 0.3y = 50; \text{60 litters of 60% solution and 40 litters of 30% solution.}

There are 3 times as many chickens as cows on a farm. If the total number of their legs is 224, how many chickens and cows are there?

\text{Let } c = \text{cows}; \text{Let } h = \text{chickens}; h = 3c; 4c + 2h = 224; \text{There are 14 cows and 42 chickens.}

Meena saves $50 every week and currently has$ 250 saved. After how many weeks will she have saved at least $1000?$

Let W = weeks; Total savings = 250 + 50W; 250 + 50W >= 1000; She will have saved at least $1000 in 15 weeks.$

A rectangle's length is 10 cm more than four times its width. If the perimeter of the rectangle is 90 cm, find the dimensions of the rectangle.

\text{Let } W = \text{width}; L = \text{length}; L = 4W + 10; 2(W + L) = 90; \text{The width is 10 cm and the length is 50 cm.}

An office manager bought 50 chairs and desks for $1100. Each desk costs$ 30 and each chair $10. How many of each were bought?$

Let C = chairs; D = desks; C + D = 50; 10C + 30D = 1100; 20 chairs and 30 desks were bought.

If three times a number decreased by 2 is 13, find the number.

\text{Let } x = \text{the number}; 3x - 2 = 13; x = 5.

A train travel a distance at 40 km/h and returns over the same distance at 60 km/h. The total time for the trip is 5 hours. Find the distance.

\text{Let } D = \text{distance}; \frac{D}{40} + \frac{D}{60} = 5; D = 120 \text{ km}

A rectangle's perimeter is 54 cm and its length is 3 cm less than twice its width. Find the rectangle's dimensions.

\text{Let } W = \text{width}; L = \text{length}; L = 2W - 3; 2(W + L) = 54; \text{The width is 9 cm and the length is 15 cm.}

Lisa has twice as many marbles as Tom. If Lisa gives 8 marbles to Tom, they will have the same number of marbles. How many marbles does each have?

Let T = Tom's marbles; L = Lisa's marbles; L = 2T; L - 8 = T + 8; Lisa has 16, Tom has 8.

During a sale, a shop offers a 20% discount on all items. After the discount, a TV costs $480. What was its original price?$

Let P = original price; P - 0.20P = 480; P = $600.$

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