simultaneous equations

A boy is 10 years older than his brother. In 4 years he will be twice as old as his brother. Find the present age of each? Let the boy's age be b and his brother's age be c. We're given two equations: b = c + 10 b + 4 = 2(c + 4) Substitute equation (1) into equation (2): (c + 10) + 4 = 2(c +...

One positive number is one-fifth of another number. The difference between the two numbers is 192, find the numbers. Let the first number be x and the second number be y. We're given two equations: x = y/5 x + y = 192 Substitute equation 1 into equation 2: y/5 + y = 192 Since 1 equals 5/5...

Mr turner sent his car to the workshop for repair work as well as to change 4 tires. Mr turner paid $1035 in all. The repair work cost 5 times the price of each tire. The mechanic told Mr. turner that the repair work cost $500. Explain the mechanic’s mistake Let the cost for work be w. Let the...

Tyrone re sells 3 pairs of Yeezys and a pair of Nikes for 250$. Nucci re sells a pair of Yeezys and Nikes for 150$ How much does a pair of Yeezys cost? Let y be the cost of Yeezy's and n be the cost of Nike's. We're given two equations: 3y + n = 250 y + n = 150 We have a system of equations...

Dina is twice as old as Andrea. The sum of their age is 72. Find their present ages. Let d be Dina's age. Let a be Andrea's age. We're given: d = 2a <-- Twice means multiply by 2 a + d = 72 Substitute equation (1) into equation (2): a + 2a = 72 Type this equation into our search engine and...

A movie theater charges 7.00 for adults and 2.00 for seniors citizens. On a day when 304 people paid for admission, the total receipt were 1118. How many who paid were adults ? How many were senior citizens? Let a be the number of adult tickets. Let s be the number of senior citizen tickets...

Ben is 4 times as old as Ishaan and is also 6 years older than Ishaan. Let b be Ben's age and i be Ishaan's age. We're given: b = 4i b = i + 6 Set (1) and (2) equal to each other: 4i = i + 6 Typing this equation into our search engine, we get: i = 2 Substitute this into equation (1): b =...

Kevin and Randy Muise have a jar containing 52 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $6.20. How many of each type of coin do they have? Let q be the number of quarters, and n be the number of nickels. We have: n + q = 52 0.05n + 0.25q =...

You earned $141 last week babysitting and cleaning. You earned $5 per hour babysitting and $7 per hour cleaning. You worked 9 more hours babysitting than cleaning. How many hours did you work last week? Let b be the hours of babysitting and c be the hours of cleaning. We're given two equations...

Max is 23 years younger than his father.Together their ages add up to 81. Let Max's age be m, and his fathers' age be f. We're given: m = f - 23 <-- younger means less m + f = 81 Substitute Equation (1) into (2): (f - 23) + f = 81 Combine like terms to form the equation below: 2f - 23 = 81...

If the perimeter of a rectangular sign is 44cm and the width is 2cm shorter than half the length, then what are the length and width? The perimeter (P) of a rectangle is: 2l + 2w = P We're given P = 44, so we substitute this into the rectangle perimeter equation: 2l + 2w = 44 We're also given...

a horse and a saddle cost $5,000. if the horse cost 4 times as much as the saddle, what was the cost of each? Let the cost of the horse be h, and the cost of the saddle be s. We're given: h + s = 5000 h = 4s Substitute equation (2) into equation (1): 4s + s = 5000 Type this equation into the...

one number is twice a second number. the sum of those numbers is 45. Let the first number be x and the second number be y. We're given: x = 2y x + y = 45 Substitute Equation (1) into Equation (2): 2y + y = 45 Typing this equation into our search engine, we get: y = 15 Plug this into...

Bob has half as many quarters as dimes. He has $3.60. How many of each coin does he have? Let q be the number of quarters. Let d be the number of dimes. We're given: q = 0.5d 0.25q + 0.10d = 3.60 Substitute (1) into (2): 0.25(0.5d) + 0.10d = 3.60 0.125d + 0.1d = 3.6 Combine like terms...

A garden table and a bench cost $977 combined. The garden table costs $77 more than the bench. What is the cost of the bench? Let the garden table cost be g and the bench cost be b. We're given b + g = 977 g = b + 77 <-- The phrase more than means we add Substitute (2) into (1): b + (b + 77)...

A father is K years old and his son is M years younger. The sum of their ages is 53. Father's Age = K Son's Age = K - M and we know K + (K - M) = 53 Combine like terms: 2K - M = 53 Add M to each side: 2K - M + M = 53 + M Cancel the M's on the left side, we get: 2K = 53+ M Divide each side...

Molly is making strawberry infused water. For each ounce of strawberry juice, she uses three times as many ounces of water as juice. How many ounces of strawberry juice and how many ounces of water does she need to make 40 ounces of strawberry infused water? Let j be the ounces of strawberry...

2 times a number added to another number is 25. 3 times the first number minus the other number is 20. Let the first number be x. Let the second number be y. We're given two equations: 2x + y = 25 3x - y = 20 Since we have matching opposite coefficients for y (1 and -1), we can add both...

Alvin is 34 years younger than Elga. Elga is 3 times older than Alvin. What is Elgas age? Let a be Alvin's age. Let e be Elga's age. We're given: a = e - 34 e = 3a Substitute (2) into (1): a = 3a - 34 Typing this equation into the search engine, we get a = 17 Subtitute this into Equation...

Anna has 50 coins in her piggy bank. She notices that she only has dimes and pennies. If she has exactly four times as many pennies as dimes, how many pennies are in her piggy bank? Let d be the number of dimes, and p be the number of pennies. We're given: d + p = 50 p = 4d Substitute (2)...