simultaneous equations

A collection of nickels and dime has a total value of $8.50. How many coins are there if there are 3 times as many nickels as dimes. Let n be the number of nickels. Let d be the number of dimes. We're give two equations: n = 3d 0.1d + 0.05n = 8.50 Plug equation (1) into equation (2) for n...

A movie theater charges $7 for adults and $3 for seniors on a particular day when 324 people paid an admission the total receipts were 1228 how many were seniors and how many were adults? Let the number of adult tickets be a. Let the number of senior tickets be s. We're given two equations: a...

Lorda is older than Kate. The sum of their ages is 30. The difference in their ages is 6. What are their ages? Let Lorda's age be l. Let Kate's age be k. We're given two equations: l + k = 30 l - k = 6 <-- Since Lorda is older Add the 2 equations together and we eliminate k: 2l = 36 Typing...

a football team won 3 more games than it lost.the team played 11 games.how many did it win? Let wins be w. Let losses be l. We're given two equations: w = l + 3 l + w = 11 Plug equation (1) into equation (2) to solve for l: l + (l + 3) = 11 Group like terms: 2l + 3 = 11 Typing this equation...

Lily needs an internet connectivity package for her firm. She has a choice between CIVISIN and GOMI with the following monthly billing policies. Each company's monthly billing policy has an initial operating fee and charge per megabyte. Operating Fee charge per Mb...

A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add their ages is equal 100 Let the man's age be m. Let the wife's age be w. Let the daughter's age be d. We're given: m = w + 5 d = 0.5m d + m + w = 100 Rearrange equation 1 in terms of w my...

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test? Let the number of true/false questions be t. Let the number of multiple choice...

If Frank’s age is double of Willis’ age and the sum of their ages is 42. What are their ages? Let Frank's age be f. Let Willis's age be w. We're given two equations: f = 2w <-- Double means multiply by 2 f + w = 42 Substitute equation (1) into equation (2): 2w + w = 42 To solve for w, type...

Jill and Jack are getting vegetables from the Farmer's Market. Jill buys 12 carrots and 8 tomatoes for $34. Jack buys 10 carrots and 7 tomatoes for $29. How much does each carrot and each tomato cost? Let the cost of carrots be c and the cost of tomatoes be t. Since the total cost is price...

At a carnival, the price of an adult ticket is $6 while a child ticket is $4. On a certain day, 30 more child tickets than adult tickets were sold. If a total of $6360 was collected from the total ticket sale that day, how many child tickets were sold? Let the number of adult tickets be a. Let...

2 times as many dimes as quarters and they have a combined value of 180 cents, how many of each coin does he have? Let d be the number of dimes. Let q be the number of quarters. We're given two equations: d = 2q 0.1d + 0.25q = 180 Substitute (1) into (2): 0.1(2q) + 0.25q = 180 0.2q + 0.25q =...

Arvin is twice as old as Cory. The sum of their ages is 42. What are their ages? Let Arvin's age be a. Let Cory's age be c. We're given two equations: a = 2c a + c = 42 Plug equation (1) into equation (2): 2c + c = 42 Plug this into our search engine and we get: c = 14 Now, we plug c = 14...

Two numbers total 12, and their differences is 20. Find the two numbers. Let the first number be x. Let the second number be y. We're given two equations: x + y = 12 x - y = 20 Since we have y coefficients of (-1 and 1) that cancel, we add the two equations together: (x + x) + (y - y) = 12 +...

10 times the first of 2 consecutive even integers is 8 times the second. Find the integers. Let the first integer be x. Let the second integer be y. We're given: 10x = 8y We also know a consecutive even integer means we add 2 to x to get y. y = x + 2 Substitute (1) into (2): 10x = 8(x + 2)...

Faith is 1/5 her mother's age. Their combined ages are 30. How old is faith? Let Faith's age be f. Let her mother's age be m. We're given: f = m/5 f + m = 30 Rearrange (1) by cross-multiplying: m = 5f Substitute this into equation (2): f + 5f = 30 Type this equation into our search engine...

The difference of two numbers is 12 and their mean is 15. Find the two numbers. Let the two numbers be x and y. We're given: x - y = 12 (x + y)/2 = 15. <-- Mean is an average Rearrange equation 1 by adding y to each side: x - y + y = y + 12 Cancelling the y's on the left side, we get: x = y...

Bob bought 10 note books and 4 pens for 18$. Bill bought 6 notebooks and 4 pens for 12$. Find the price of one note book and one pen. Let the price of each notebook be n. Let the price of each pen be p. We're given two equations: 10n + 4p = 18 6n + 4p = 12 Since we have matching coefficients...

Jack has 34 bills and coins in 5’s and 2’s. The total value is $116. How many 5 dollar bills does he have? Let the number of 5 dollar bills be f. Let the number of 2 dollar bills be t. We're given two equations: f + t = 34 5f + 2t = 116 We have a system of equations, which we can solve 3...

A first number plus twice a second number is 3. Twice the first number plus the second totals 24. Let the first number be x. Let the second number be y. We're given: x + 2y = 3 <-- Because twice means multiply by 2 2x + y = 24 <-- Because twice means multiply by 2 We have a system of...

The senior class at high school A and high school B planned separate trips to the state fair. There senior class and high school A rented and filled 10 vans and 6 buses with 276 students. High school B rented and filled 5 vans and 2 buses with 117 students. Every van had the same number of...