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# simultaneous equations

1. ### Connor runs 2 mi more each day than David. The sum of the distances they run each week is 56 mi. How

Connor runs 2 mi more each day than David. The sum of the distances they run each week is 56 mi. How far does David run each day? Let Connor's distance be c Let David's distance be d We're given two equations: c = d + 2 7(c + d) = 56 Simplifying equation 2 by dividing each side by 7, we get...
2. ### the cost of a buffet at a restaurant is different for adults and kids. the bill for 2 adults and 3 k

the cost of a buffet at a restaurant is different for adults and kids. the bill for 2 adults and 3 kids is \$51. the bill for 3 adults and 1 kid is \$45. what is the cost per adult and per kid? Let the cost for each adult be a Let the cost for each kid be k We're given two equations: 2a + 3k =...
3. ### Jennifer is twice as old as Peter. The difference between their ages is 15. What is Peters age

Jennifer is twice as old as Peter. The difference between their ages is 15. What is Peters age Let j be Jennifer's age Let p be Peter's age We're given two equations: j = 2p j - p = 15 Substitute equation (1) into equation (2) for j 2p - p = 15 To solve for p, we type this equation into our...
4. ### Consider the following 15 numbers 1, 2, y - 4, 4, 5, x, 6, 7, 8, y, 9, 10, 12, 3x, 20 - The mean o

Consider the following 15 numbers 1, 2, y - 4, 4, 5, x, 6, 7, 8, y, 9, 10, 12, 3x, 20 - The mean of the last 10 numbers is TWICE the mean of the first 10 numbers - The sum of the last 2 numbers is FIVE times the sum of the first 3 numbers (i) Calculate the values of x and y We're given two...
5. ### The length of a rectangle is equal to triple the width. Find the length of the rectangle if the peri

The length of a rectangle is equal to triple the width. Find the length of the rectangle if the perimeter is 80 inches. The perimeter (P) of a rectangle is: 2l + 2w = P We're given two equations: l = 3w 2l + 2w = 80 We substitute equation 1 into equation 2 for l: 2(3w) + 2w = 80 6w + 2w = 80...
6. ### Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appr

Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appropriate pair of equations. Let Cam's age be c. Let Lara's age be l. We're given two equations: c = l + 3 (Since older means we add) c + l = 63 To solve this system of equations, we...
7. ### A woman is one-half as old as her mother. The sum of their ages is 75. What are their ages?

A woman is one-half as old as her mother. The sum of their ages is 75. What are their ages? Let the woman's age be w. Let the mother's age be m. We're given two equations: w = m/2 m + w = 75 Substitute equation (1) into equation (2) for w: m + m/2 = 75 To solve for m, we type this equation...
8. ### The average height of a family of 6 is 6 feet. After the demise of the mother, the average height re

The average height of a family of 6 is 6 feet. After the demise of the mother, the average height remained the same. What is the height of the mother? Let the height of the family without the mom be f. Let the height of the mother be m. Averages mean we add the heights and divide by the...
9. ### A bag of quarters and nickels is worth \$8.30. There are two less than three times as many quarters a

A bag of quarters and nickels is worth \$8.30. There are two less than three times as many quarters as nickels. How many of the coins must be quarters? Assumptions and givens: Let the number of quarters be q Let the number of nickels be n We have two equations: 0.05n + 0.25q = 8.30 n = 3q - 2...
10. ### A straight line has the equation ax + by=23. The points (5,-2) and (1,-5) lie on the line. Find the

A straight line has the equation ax + by=23. The points (5,-2) and (1,-5) lie on the line. Find the values of a and b. plug in both points and form 2 equations: 5a - 2b = 23 1x - 5b = 23 We can solve this simultaneous equations any one of three ways: Substitution Method Elimination Method...
11. ### 2 pens and 1 eraser cost \$35 and 3 pens and 4 erasers cost \$65. X represents the cost of 1 pen and Y

2 pens and 1 eraser cost \$35 and 3 pens and 4 erasers cost \$65. X represents the cost of 1 pen and Y represents the cost of 1 eraser. Write the 2 simultaneous equations and solve. Set up our 2 equations where cost = price * quantity: 2x + y = 35 3x + 4y = 65 We can solve this one of three...
12. ### Building A is 150 feet shorter than Building B. The height of both building is 1530 feet. Find the h

Building A is 150 feet shorter than Building B. The height of both building is 1530 feet. Find the height of both building A and B. Let a be the height of building A Let b be the height of building B We're given two equations: a = b - 150 a + b = 1530 To solve this system of equations, we...
13. ### The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages?

The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages? Givens Let Mr. Adam's age be a Let Mrs. Benson's age be b We're given two equations where sum means we add and difference means we subtract: a + b = 55 a - b = 3 Since we have opposite coefficients...
14. ### at a bakery the cost of one cupcake and 2 slices of pie is \$12.40. the cost of 2 cupcakes and 3 slic

at a bakery the cost of one cupcake and 2 slices of pie is \$12.40. the cost of 2 cupcakes and 3 slices of pie costs \$20.20. what is the cost of one cupcake? Let the number of cupcakes be c Let the number of pie slices be p Total Cost = Unit cost * quantity So we're given two equations: 1c +...
15. ### Some History teachers at Richmond High School are purchasing tickets for students and their adult ch

Some History teachers at Richmond High School are purchasing tickets for students and their adult chaperones to go on a field trip to a nearby museum. For her class, Mrs. Yang bought 30 student tickets and 30 adult tickets, which cost a total of \$750. Mr. Alexander spent \$682, getting 28 student...
16. ### The sum of Jocelyn and Joseph's age is 40. In 5 years, Joseph will be twice as Jocelyn's present age

The sum of Jocelyn and Joseph's age is 40. In 5 years, Joseph will be twice as Jocelyn's present age. How old are they now? Let Jocelyn's age be a Let Joseph's age be b. We're given two equations: a + b = 40 2(a + 5) = b + 5 We rearrange equation (1) in terms of a to get: a = 40 - b 2a = b...
17. ### Rico was born 6 years after Nico. The sum of their age is 36. How old is Nico?

Rico was born 6 years after Nico. The sum of their age is 36. How old is Nico? Let Rico's age be r Let Nico's age be n We're given two equations: r = n + 6 n + r = 36 We plug equation (1) into equation (2) for r: n + n + 6 = 36 To solve this equation for n, we type it in our search engine...
18. ### The Radio City Music Hall is selling tickets to Kayla’s premiere at the Rockettes. On the first day

The Radio City Music Hall is selling tickets to Kayla’s premiere at the Rockettes. On the first day of ticket sales they sold 3 senior citizen tickets and 9 child tickets for a total of \$75. It took in \$67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the...
19. ### A first number plus twice a second number is 14. Twice the first number plus the second totals 40. F

A first number plus twice a second number is 14. Twice the first number plus the second totals 40. Find the numbers. Givens and assumptions: Let the first number be x. Let the second number be y. Twice means multiply by 2 The phrases is and totals mean equal to We're given two equations: x...
20. ### On Monday the office staff at your school paid 8.77 for 4 cups of coffee and 7 bagels. On Wednesday

On Monday the office staff at your school paid 8.77 for 4 cups of coffee and 7 bagels. On Wednesday they paid 15.80 for 8 cups of coffee and 14 bagels. Can you determine the cost of a bagel Let the number of cups of coffee be c Let the number of bagels be b. Since cost = Price * Quantity, we're...