simultaneous equations

Nancy is 10 years less than 3 times her daughters age. If Nancy is 41 years old, how old is her daughter? Declare variables for each age: Let Nancy's age be n Let her daughter's age be d We're given two equations: n = 3d - 10 n = 41 We set 3d - 10 = 41 and solve for d: Solve for d in the...

larger of 2 numbers is 12 more than the smaller number. if the sum of the 2 numbers is 74 find the 2 numbers Declare Variables for each number: Let l be the larger number Let s be the smaller number We're given two equations: l = s + 12 l + s = 74 Equation (1) already has l solved for...

A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children. What was the cost of each ticket? Declare variables: Let a be the number of adult's tickets Let c be the number of children's tickets Cost = Price * Quantity We're given two equations: a +...

a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age. Declare variables: Let f be the father's age Let s be the son's age We're given two equations: s = f/4 f - s = 30. The reason why we subtract s from f is the father is older Using substitution, we...

larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number? Declare variables for the 2 numbers: Let l be the larger number Let s be the smaller number We're given two equations: l = s + 4 l + s = 40 To get this problem in terms of the larger number...

In a class there are 5 more boys than girls. There are 13 students in all. How many boys are there in the class? We start by declaring variables for boys and girls: Let b be the number of boys Let g be the number of girls We're given two equations: b = g + 5 b + g = 13 Substitute equation...

2 numbers that are equal have a sum of 60 Let's choose 2 arbitrary variables for the 2 numbers x, y Were given 2 equations: x = y <-- Because we have the phrase that are equal x + y = 60 Because x = y in equation (1), we can substitute equation (1) into equation (2) for x: y + y = 60 Add...

Alberto and Willie each improved their yards by planting daylilies and ivy. They bought their supplies from the same store. Alberto spent $64 on 3 daylilies and 8 pots of ivy. Willie spent $107 on 9 daylilies and 7 pots of ivy. What is the cost of one daylily and the cost of one pot of ivy...

kate is twice as old as her sister mars. the sum of their ages is 24. find their ages. Let k be Kate's age Let m be Mars's age We're given two equations: k = 2m. (Because twice means multiply by 2) k + m = 24 Substitute equation (1) for k into equation (2): 2m + m = 24 T o solve for m, we...

According to the American Bureau of Labor Statistics, you will devote 32 years to sleeping and eating. The number of years sleeping will exceed the number of years eating by 24. Over your lifetime, how many years will you spend on each of these activities? Assumptions: Let years eating be e...

numerator of a fraction is 5 less than its denominator. if 1 is added to the numerator and to the denominator the new fraction is 2/3. find the fraction. Let n be the numerator. Let d be the denominator. We're given 2 equations: n = d - 5 (n + 1)/(d + 1) = 2/3 Substitute equation (1) into...

At the end of the 2021 NBA season, the NY Knicks had 10 more wins than losses. This NBA season the NY Knicks played a total of 72 times. Find a solution to this problem and explain. Let w be the number of wins Let l be the number of losses We're given two equations: w = l + 10 l + w = 72 To...

A man is four time as old as his son. How old is the man if the sum of their ages is 60? Let the son's age be a. Then the man's age is 4a. If the sum of their ages is 60, we have: a + 4a = 60 To solve this equation for a, we type it in our math engine and we get: a = 12 Therefore, the man's...

Justin is older than Martina. The difference in their ages is 22 and the sum of their ages is 54. What age is Martina? Assumptions and givens: Let Justin's age be j Let Martina's age be m j > m (since Justin is older than Martina) We're given the following equations : j - m = 22 j + m = 54...

Cars and trucks are the most popular vehicles. last year, the number of cars sold was 39,000 more than 3 times the number of trucks sold. There were 216,000 cars sold last year. Write an equation that can be used to find the number of trucks, t, sold last year. Let c be the number of cars. Let...

Antonio has a change jar that contains $3.65 in half dollars and nickels. He has 7 more nickels than half dollars. How many of each type of coin does he have? Let h be half dollars Let n be nickels We're given two equations: n = h + 7 0.5h + 0.05n = 3.65 Substitute equation (1) into equation...

Jenny threw the javelin 4 metres further than Angus but 5 metres less than Cameron. if the combined distance thrown by the 3 friends is 124 metres, how far did Angus throw the javelin? Assumptions and givens: Let a be the distance Angus threw the javelin Let c be the distance Cameron threw the...

a is 2 years older than b who is twice as old as c. if the total ages of a,b and c is 42, then how old is b We're given 3 equations: a = b + 2 b = 2c a + b + c = 42 Substituting equation (2) into equation (1), we have: a = 2c + 2 Since b = 2c, we substitute both of these into equation (3) to...

A first number plus twice a second number is 10. Twice the first number plus the second totals 35. Find the numbers. The phrase a number means an arbitrary variable A first number is written as x A second number is written as y Twice a second number means we multiply y by 2: 2y A first number...

Bud makes $400 more per month than maxine If their total income is $3600 how much does bud earn per month Let Bud's earnings be b. Let Maxine's earnings be m. We're given two equations: b = m + 400 b + m = 3600 To solve this system of equations, we substitute equation (1) into equation (2)...