simultaneous equations

$3.75 in quarters and nickels in her car. The number of nickels is fifteen more than the number of quarters. How many of each type of coin does she have? Let the number of nickels be n, and the number of quarters be q. We know nickels are 0.05, and quarters are 0.25. We're given: n = q + 15...

A crate contains 300 coins and stamps. The coins cost $3 each and the stamps cost $1.5 each. The total value of the items is $825. How many coins are there? Let c be the number of coins, and s be the number of stamps. We're given: c + s = 300 3c + 1.5s = 825 We have a set of simultaneous...

Half of a pepperoni pizza plus 3/4ths of a ham and pineapple pizza has 765 calories. 1/4th of a pepperoni pizza and a whole ham and pineapple pizza contains 745 calories. How many calories are each of the 2 kinds of pizzas individually? Let p be the pepperoni pizza calories and h be the ham and...

An isosceles triangles non-congruent angle is 16 more than twice the congruent ones. What is the measure of all 3 angles? Let the congruent angles measurement be c. And the non-congruent angle measurement be n. We're given: n = 2c + 16 <-- Twice means we multiply by 2, and more than means we...

A person invested 30,000 in stocks and bonds. Her investment in bonds is 2000 more than 1-third her investments in stocks. How much did she invest in stocks? How much did she invest in bonds? Let the stock investment be s, and the bond investment be b. We're given: b + s = 30000 b = 1/3s +...

Rachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On Wednesday, she sold 6 fewer books than she did on Tuesday. During the 3 days Rachel sold 19 books. Create an equation that can be used to find m, a number of books Rachel sold on Monday. Let me be the...

The sum of 2 consecutive numbers is 3 less than 3 times the first number. What are the numbers? Let the first number be x. And the second number be y. We're given: y = x + 1 x + y = 3x - 3 (less 3 means subtract 3) Substitute (1) into (2): x + x + 1 = 3x - 3 Combine like terms: 2x + 1 = 3x...

The difference between 2 numbers is 108. 6 times the smaller is equal to 2 more than the larger. What are the numbers? Let the smaller number be x. Let the larger number be y. We're given: y - x = 108 6x = y + 2 Rearrange (1) by adding x to each side: y = x + 108 Substitute this into (2)...

Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. Which equation could be used to find Jeremy's age, j, if he is the younger man. Let Sam's age be s. Let' Jeremy's age be j. We're given: s = j + 2 <-- consecutive odd integers sj = 783 Substitute...

Kate spent 1 more than Lauren, and together they spent 5. Let k be the amount Kate spent, and l be the amount Lauren spent. We're given: k = l + 1 k + l = 5 Substitute (1) into (2): (l + 1) + l = 5 Group like terms 2l + 1 = 5 Typing this equation into our search engine, we get: l = 2 Plug...

The sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 times the unit digit. Find the number. Let the digits be (x)(y) where t is the tens digit, and o is the ones digit. We're given: x + y = 10 10x+ y = 15y + 4 Simplifying Equation (2) by subtracting y...

the sum of 2 numbers is 5. 5 times the larger number plus 4 times the smaller number is 37. Find the numbers Let the first small number be x. Let the second larger number be y. We're given: x + y = 5 5y + 4x = 37 We can solve this 3 ways, using the following methods: Substitution Method...

Twice a first number decreased by a second number is 16. The first number increased by 3 times the second number is 1. Find the numbers. Let the first number be x and the second number be y. We're given: 2x - y = 16 x + 3y = 1 Using our simultaneous equations calculator, you can solve this 3...

Kelly took clothes to the cleaners 3 times last month. First, she brought 4 shirts and 1 pair of slacks and paid11.45. Then she brought 5 shirts, 3 pairs of slacks, and 1 sports coat and paid 27.41. Finally, she brought 5 shirts and 1 sports coat and paid 16.94. How much was she charged for each...

A cashier has a total of 52 bills in her cash drawer. There are only $10 bills and $5 bills in her drawer. The value of the bills is $320. How many $10 bills are in the drawer? Let f be the amount of $5 bills in her drawer. Let t be the amount of $10 bills in her drawer. We're given two...

The team A scored 13 more points than Team B. The total of their score was 47. How many points did team A score? Let a be the amount of points A scored, and b be the amount of points B scored. We're given: a = b + 13 a + b = 47 Plug (1) into (2) (b + 13) + b = 47 Combine like terms: 2b + 13...

One number exceeds another by 15. The sum of the numbers is 51. What are these numbers? Let the first number be x, and the second number be y. We're given two equations: x = y + 15 x + y = 51 Plug (1) into (2) (y + 15) + y = 51 Combine like terms: 2y + 15 = 51 Plug this equation into the...

One number is 8 times another number. The numbers are both positive and have a difference of 70. Let the first number be x, the second number be y. We're given: x = 8y x - y = 70 Substitute(1) into (2) 8y - y = 70 Plugging this equation into our search engine, we get: y = 10 <-- This is the...

A high school graduating class is made up of 440 students. There are 168 more girls than boys. How many boys are in the class? Let b be the number of boys and g be the number of girls. We're given 2 equations: b + g = 440 g = b + 168 Substitute (2) into (1) b + (b + 168) = 440 Combine like...

Nick said that his sister is 4 times as old as his brother, and together their ages add to 20 complete this equation to find his brothers age Let b be the brother's age and s be the sister's age. We're given two equations: s =4b b + s = 20 Plug (1) into (2): b + 4b = 20 Type this equation...