system of equations

a large fry has 120 more calories than a small. 5 large fries is the same amount of calories as 7 small. How many calories does each size fry have? Let the number of calories in large fries be l. Let the number of calories in small fries be s. We're given two equations: l = s + 120 5l = 7s...

The bigger of 2 numbers in 5 larger than the smaller. Twice the smaller, increased by, twice the larger, is equal to 50. Find each number. Let the big number be b. Let the small number be s. We're given two equations: b = s + 5 2s + 2b = 50 Substitute equation (1) into equation (2) 2s + 2(s +...

Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he is able to buy 5 packages of paper and 6 staplers for $62. How much does a package of paper cost? How much does a stapler cost? Let the cost of paper packages be p and the cost of staplers be s...

One number is 3 times another. Their sum is 44. Let the first number be x, and the second number be y. We're given: x = 3y x + y = 44 Substitute (1) into (2): 3y + y = 44 Type this equation into the search engine, and we get: y = 11 Plug this into equation (1): x = 3(11) x = 33

Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years. Let Victoria's age be v. And her neighbor's age be n. We're given: v = n + 4 v + n <=14 <-- no more than means less than or equal to Substitute Equation (1) into Inequality (2): (n + 4) + n <= 14...

The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. How old are the cousins? Let a be Suresh's age, h be Hakima's age, and c be Saad's age. We're given: a + h + c = 48 a = 0.5h a = c + 4 To isolate equations in terms of Suresh's age (a), let's do...

2 numbers add to 200. The first is 20 less than the second. Let the first number be x and the second number be y. We're given: x + y = 200 x = y - 20 Plug (2) into (1) (y - 20) + y = 200 Group like terms: 2y - 20 = 200 Typing this equation into our search engine, we get: y = 110 <-- This...

An irregular pentagon is a five sided figure. The two longest sides of a pentagon are each three times as long as the shortest side. The remaining two sides are each 8m longer than the shortest side. The perimeter of the Pentagon is 79m. Find the length of each side of the Pentagon. Let long...

There are two numbers. The sum of 4 times the first number and 3 times the second number is 24. The difference between 2 times the first number and 3 times the second number is 24. Find the two numbers. Let the first number be x and the second number be y. We have 2 equations: 4x + 3y = 24 2x...

Jim is 9 years older than June. Alex is 8 years younger than June. If the total of their ages is 82, how old is the eldest of them Let j be Jim's age, a be Alex's age, and u be June's age. We have 3 given equations: j + a + u = 82 j = u + 9 a = u - 8 Substitute (2) and (3) into (1) (u + 9) +...

The difference between two positive numbers is 5 and the square of their sum is 169. Let the two positive numbers be a and b. We have the following equations: a - b = 5 (a + b)^2 = 169 Rearrange (1) by adding b to each side. We have a = b + 5 Now substitute (3) into (2): (b + 5 + b)^2 = 169...

The sum of three numbers is 171. The second number is 1/2 of the first and the third is 3/4 of the first. Find the numbers. We have three numbers, x, y, and z. x + y + z = 171 y = 1/2x z = 3/4x Substitute (2) and (3) into (1) x + 1/2x + 3/4x = 171 Use a common denominator of 4 for each x...

Tom is 2 years older than Sue and Bill is twice as old as Tom. If you add all their ages and subtract 2, the sum is 20. How old is Bill? Let t be Tom's age., s be Sue's age, and b be Bill's age. We have the following equations: t = s + 2 b = 2t s + t + b - 2 = 20 Get (2) in terms of s (2) b...

Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old. How old is Barbara? Let a be Alice's age, b be Barbara's age, and c be Carol's age. We have 3 given equations: a = b - 3 b = c - 5 a + b + c = 68 Rearrange (2) c = b + 5...

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Hugo is going to send some flowers to his wife. Somerville Florist charges $2 per rose, plus $39 for the vase. Dwaynes Flowers, in contrast, charges $3 per rose and $10 for the vase. If...

Jenny went shoe shopping. Now she has 5 more pairs than her brother. Together they have 25 pairs. How many pairs does Jenny have and how many pairs does her brother have? Let j be the number of shoes Jenny has and b be the number of s hoes her brother has. Set up 2 equations: (1) b + j = 25 (2)...

The length of the flag is 2 cm less than 7 times the width. The perimeter is 60cm. Find the length and width. A flag is a rectangle shape. So we have the following equations Since P = 2l + 2w, we have 2l + 2w = 60 l = 7w - 2 Substitute Equation 1 into Equation 2: 2(7w -2) + 2w = 60 14w - 4 +...

Mr. Winkle downloaded 34 more songs than Mrs. Winkle downloaded. Together they downloaded 220 songs. How many songs did each download? Let x = Mr. Winkle downloads and y = Mrs. Winkle downloads. We then have x = y + 34 and x + y = 220. Substitute equation 1 into equation 2, we have: (y +...