simultaneous equations

Dan's school is planning a field trip to an art museum. Bus company A charges a $60 rental fee plus $4 per student. Bus company B charges $150 plus $2 per student. How many students would have to go for the cost to be the same? Set up Company A's cost equation C(s) where s is the number of...

A cashier has 44 bills, all of which are $10 or $20 bills. The total value of the money is $730. How many of each type of bill does the cashier have? Let a be the amount of $10 bills and b be the amount of $20 bills. We're given two equations: a + b = 44 10a + 20b = 730 We rearrange equation...

A carpenter wants to cut a 45 inch board into two pieces such that the longer piece will be 7 inches longer than the shorter. How long should each piece be Let the shorter piece of board length be s. Then the larger piece is: l = s + 7 And we know that: Shorter Piece + Longer Piece = 25...

Sherry is 31 years younger than her mom. The sum of their ages is 61. How old is Sherry? Let Sherry's age be s. Let the mom's age be m. We're given two equations: s = m - 31 m + s = 61 Substitute equation (1) into equation (2) for s: m + m - 31 = 61 To solve for m, we type this equation into...

Bob is twice as old as Henry. The sum of their ages is 42. How old is Henry? Let Bob's age be b. Let Henry's age be h. We're given two equations: b = 2h b + h = 42 Substitute b = 2h in equation 1 into equation 2 for b: 2h + h = 42 To solve for h, we type this equation into our search engine...

In a bike shop they sell bicycles & tricycles. I counted 80 wheels & 34 seats. How many bicycles & tricycles were in the bike shop? Let b be the number or bicycles and t be the number of tricycles. Since each bicycle has 2 wheels and 1 seat and each tricycle has 3 wheels and 1 seat, we have...

46 people showed up to the party. There were 8 less men than women present. How many men were there? Let the number of men be m. Let the number of women be w. We're given two equations: m = w - 8 (8 less men than women) m + w = 46 (46 showed up to the party) Substitute equation (1) into...

A class has 35 boys and girls. There are 7 more girls than boys. Find the number of girls and boys in the class Let the number of boys be b and the number of girls be g. We're given two equations: b + g = 35 g = b + 7 (7 more girls means we add 7 to the boys) To solve for b, we substitute...

A girl is three years older than her brother. If their combined age is 35 years, how old is each Let the girl's age be g. Let the boy's age be b. We're given two equations: g = b + 3 (Older means we add) b + g = 35 Now plug in equation (1) into equation (2) for g: b + b + 3 = 35 To solve...

Clark wants to give some baseball cards to his friends. If he gives 6 cards to each of his friends, he will have 5 cards left. If he gives 8 cards to each of his friends, he will need 7 more cards. How many friends is the giving the cards to? Let the number of friends Clark gives his cards to...

Martha is 18 years older than Harry. Their ages add to 106. Write an equation and solve it to find the ages of Martha and Harry. Let m be Martha's age. Let h be Harry's age. We're given two equations: m = h + 18 (older means we add) h + m = 106 Substitute equation (1) into equation (2) for m...

Daniel is 6cm taller than Kamala. If their total height is 368cm, how tall is Kamala? Let Daniel's height be d. Let Kamala's height be k. We're given two equations: d = k + 6 d + k = 368 Substitute equation (1) into equation (2) for d: k + 6 + k = 368 To solve for k, we type this equation...

A problem states: "There are 9 more children than parents in a room. There are 25 people in the room in all. How many children are there in the room?" Let the number of children be c. Let the number of parents be p We're given: c = p + 9 (9 more children than parents) c + p = 25 to solve...

414 people used public pool. Daily prices are $1.75 for children and $2.00 for adults. Total cost was $755.25. How many adults and children used the pool Let the number of children who used the pool be c, and the number of adults who used the pool be a. We're given two equations: a + c = 414...

At a homecoming football game, the senior class sold slices of pizza for $.75 each and hamburgers for $1.35 each. They sold 40 more slices of pizza than hamburgers, and sales totaled $292.5. How many slices of pizza did they sell Let the number of pizza slices be p and the number of hamburgers...

The difference between two numbers is 25. The smaller number is 1/6th of the larger number. What is the value of the smaller number Let the smaller number be s. Let the larger number be l. We're given two equations: l - s = 25 s = l/6 Plug in equation (2) into equation (1): l - l/6 = 25...

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 327 people entered the park , and the admission fee collected totaled 978.00 dollars . How many children and how many adults were admitted? Let the number of children's tickets be c. Let the number...

An orchard has 816 apple trees. The number of rows exceeds the number of trees per row by 10. How many trees are there in each row? Let the rows be r and the trees per row be t. We're given two equations: rt = 816 r = t + 10 Substitute equation (2) into equation (1) for r: (t + 10)t = 816...

The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. How old is Levi now? Let Levi's current age be l. Let Renee's current age be r. Were given two equations: l + r = 89 l - 7 = 4(r - 7) Simplify equation 2 by multiplying through: l + r = 89 l - 7...

admission to the school fair is $2.50 for students and $3.75 for others. if 2848 admissions were collected for a total of 10,078.75, how many students attended the fair Let the number of students be s and the others be o. We're given two equations: o + s = 2848 3.75o + 2.50s = 10078.75 Since...