simultaneous equations

The length of a rectangle is 6 less than twice the width. If the perimeter is 60 inches, what are the dimensions? Set up 2 equations given P = 2l + 2w: l = 2w - 6 2l + 2w = 60 Substitute (1) into (2) for l: 2(2w - 6) + 2w = 60 4w - 12 + 2w = 60 6w - 12 = 60 To solve for w, type this into our...

The length of a rectangle is three times its width.If the perimeter is 80 feet, what are the dimensions? We're given 2 equations: l = 3w P = 80 = 2l + 2w = 80 Substitute (1) into (2) for l: 2(3w) + 2w = 80 6w + 2w = 80 8w = 80 Divide each side by 8: 8w/8 = 80/8 w = 10 Substitute w = 10 into...

Let x be the larger number. Let y be the smaller number. We're given two equations: x + y = 231 x = 2y Substitute (2) into (1) for x: 2y + y = 231 3y = 231 Type this into our math solver and get y = 77 This means x is: x = 2(77) x = 154

There are 812 students in a school. There are 36 more girls than boys. How many girls are there? Let b be boys Let g be girls We're given two equations: b + g = 812 g = b + 36 Rearrange equation 2 to subtract b from each side: b + g = 812 -b + g = 36 Add equation (1) to equation (2): b...

Let a be the cost of the ball and b be the cost of the bat: We're given 2 equations: a + b = 1.10 b = a + 1 Substitute equation (2) into equation (1) for b: a + a + 1 = 1.10 Combine like terms: 2a + 1 = 1.10 Subtract 1 from each side: 2a + 1 - 1 = 1.10 - 1 2a = 0.10 Divide each side by 2...

The difference between two numbers is 96. One number is 9 times the other. What are the numbers? Let x be the first number Let y be the second number We're given two equations: x - y = 96 x = 9y Substitute equation (2) into equation (1) for x 9y - y = 96 Plugging this equation into our math...

A dog and a cat together cost $100. If the price of the dogs $90 more than the cat, what is the cost of the cat? Set up givens and equations Let the cost of the dog be d Let the cost of the cat be c We're given 2 equations: c + d = 100 d = c + 90 Substitute equation (2) into equation (1)...

Jason has an equal number of nickels and dimes. The total value of his nickels and dimes is $2.25. How many nickels does Jason have? Let the number of nickels be n Let the number of dimes be d We're given two equations: d = n 0.05n + 0.1d = 2.25 Substitute equation (1) for d into equation...

Luke and Dan's total debt is $72. If Luke's debt is three times Dan's debt, what is Dan's debt? Let Dan's debt be d. Let Luke's debt be l. We're given two equations: d + l = 72 l = 3d Substitute equation (2) for l into equation (1): d + 3d = 72 Solve for d in the equation d + 3d = 72 Step...

The price of a cheap backpack is $15 less than an expensive backpack. When Emily bought both, she paid $75. What is the cost of the cheap backpack? backpack cost = b Cheap backpack = b - 15 The total of both items equals 75: b + b - 15 = 75 Solve for b in the equation b + b - 15 = 75 Step 1...

Jane is twice a old as Joel. If their ages total 63, how old is Joel? Joel = j Jane = 2j j + 2j = 63 3j = 63 Divide each side by 3: 3j/3 = 63/j Cancel the 3's on the left side: j = 21

Stanley bought a ruler and a yardstick for $1.25. If the yardstick cost 45 cents more than the ruler, what was the cost of the yardstick? Let r be the cost of the ruler Let y be the cost of the yardstick We're given 2 equations: r + y = 1.25 y = r + 0.45 Substitute equation (2) into equation...

Laura weighs 45 pounds more than her pet dog. When they are on the scale together, they weigh 85 pounds. How much does Laura weigh? Let Laura weigh l and her dog weigh d. WE have: l = d + 45 d + l = 85 Substitute equation (1) into Equation (2) for l: d + d + 45 = 85 Solve for d in the...

two numbers have an average of 2100 and one number is $425 more than the other number. What are the numbers Let the first number be x and the second number be y. We're given two equations: (x + y)/2 = 2100 (Average) y = x + 425 Rearrange equation (1) by cross multiplying x + y = 2 * 2100 x +...

A 100 point test contains a total of 20 questions. The multiple choice questions are worth 3 points each and short response questions are worth 8 points each. Write a system of linear equations that represents this situation Assumptions: Let m be the number of multiple choice questions Let s...

Length (l) is the same as width (w) and their product is 64. We're given 2 equations: lw = 64 l = w Substitute equation (2) into equation (1): w * w = 64 w^2 = 64 w = 8 Since l = w, then l = 8

2 baseball players hit 60 home runs combined last season. The first player hit 3 more home runs than twice a number of home runs the second player hit. how many home runs did each player hit? Declare variables: Let the first players home runs be a Let the second players home runs be b We're...

Kiko is now 6 times as old as his sister. In 6 years, he will be 3 times as old as his sister. What is their present age? Let k be Kiko's present age Let s be Kiko's sisters age. We're given two equations: k = 6s k + 6 = 3(s + 6) To solve this system of equations, we substitute equation (1)...

A 98-inch piece of wire must be cut into two pieces. One piece must be 10 inches shorter than the other. How long should the pieces be? The key phrase in this problem is two pieces. Declare Variables: Let the short piece length be s Let the long piece length be l We're given the following s...

The volleyball team and the wrestling team at Clarksville High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $4 per car. In addition, they have already brought in $81 from past fundraisers. The wrestling team has raised $85 in the past...