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# simultaneous equations

1. ### there are \$4.20 in nickel and quarters. There are 6 more nickels than quarters there. How many coins

there are \$4.20 in nickel and quarters. There are 6 more nickels than quarters there. How many coins of each are there We're given two equations: n = q + 6 0.05n + 0.25q = 4.2 Substitute equation (1) into equation (2): 0.05(q + 6) + 0.25q = 4.2 Multiply through and simplify: 0.05q + 0.3 +...
2. ### 2 numbers that add up makes 5 but multiplied makes -36

2 numbers that add up makes 5 but multiplied makes -36 Let the first number be x and the second number be y. We're given two equations: x + y = 5 xy = -36 Rearrange equation (1) by subtracting y from each side: x = 5 - y xy = -36 Substitute equation (1) for x into equation (2): (5 - y)y =...
3. ### Germany and Austria have a total of 25 states. Germany has 7 more states than Austria has. Create 2

Germany and Austria have a total of 25 states. Germany has 7 more states than Austria has. Create 2 equations. Let g be the number of German states. Let a be the number of Austrian states. We're given two equations: a + g = 25 g = a + 7 To solve this system of equations, we substitute...
4. ### eric is twice as old as Shawn. The sum of their ages is 33. How old is Shawn?

eric is twice as old as Shawn. The sum of their ages is 33. How old is Shawn? Let Eric's age be e. Let Shawn's age be s. We're given two equations: e = 2s e + s = 33 Substitute equation (1) into equation (2) for e so we can solve for s: 2s + s = 33 To solve for s, we type this equation into...
5. ### A food truck sells salads for \$6.50 each and drinks for \$2.00 each. The food trucks revenue from sel

A food truck sells salads for \$6.50 each and drinks for \$2.00 each. The food trucks revenue from selling a total of 209 salads and drinks in one day was \$836.50. How many salads were sold that day? Let the number of drinks be d. Let the number of salads be s. We're given two equations: 2d +...
6. ### Andrea has one hour to spend training for an upcoming race she completes her training by running ful

Andrea has one hour to spend training for an upcoming race she completes her training by running full speed in the distance of the race and walking back the same distance to cool down if she runs at a speed of 9 mph and walks back at a speed of 3 mph how long should she plan on spending to walk...
7. ### Your friends in class want you to make a run to the vending machine for the whole group. Everyone pi

Your friends in class want you to make a run to the vending machine for the whole group. Everyone pitched in to make a total of \$12.50 to buy snacks. The fruit drinks are \$1.50 and the chips are \$1.00. Your friends want you to buy a total of 10 items. How many drinks and how many chips were you...
8. ### A store sells small notebooks for \$6 and large notebooks for \$12. If a student buys 6 notebooks and

A store sells small notebooks for \$6 and large notebooks for \$12. If a student buys 6 notebooks and spends \$60, how many of each did he buy? Let the amount of small notebooks be s. Let the amount of large notebooks be l. We're given two equations: l + s = 6 12l + 6s = 60 Multiply equation (1)...
9. ### one number is 3 times as large as another. Their sum is 48. Find the numbers

one number is 3 times as large as another. Their sum is 48. Find the numbers Let the first number be x. Let the second number be y. We're given two equations: x = 3y x + y = 48 Substitute equation (1) into equation (2): 3y + y = 48 To solve for y, we type this equation into the search engine...
10. ### A first number plus twice a second number is 6. Twice the first number plus the second totals 15. Fi

A first number plus twice a second number is 6. Twice the first number plus the second totals 15. Find the numbers. Let the first number be x. Let the second number be y. We're given two equations: x + 2y = 6 2x + y = 15 Multiply the first equation by -2: -2x - 4y = -12 2x + y = 15 Now add...
11. ### Sam has \$2.25 in quarters and dimes, and the total number of coins is 12. How many quarters and how

Sam has \$2.25 in quarters and dimes, and the total number of coins is 12. How many quarters and how many dimes? Let d be the number of dimes. Let q be the number of quarters. We're given two equations: 0.1d + 0.25q = 2.25 d + q = 12 We have a simultaneous system of equations. We can solve...
12. ### Grandmother, mother and daughter are celebrating 150 years of life. The Mother is 25 years older tha

Grandmother, mother and daughter are celebrating 150 years of life. The Mother is 25 years older than her daughter, but 31 years younger than her mother (the grandmother). How old are the three Let grandmother's age be g. Let mother's age be m. Let daughter's age be d. We're given 3 equations...
13. ### Nicole is half as old as Donald. The sum of their ages is 72. How old is Nicole in years?

Nicole is half as old as Donald. The sum of their ages is 72. How old is Nicole in years? Let n be Nicole's age. Let d be Donald's age. We're given two equations: n = 0.5d n + d = 72 Substitute equation (1) into (2): 0.5d + d = 72 1.5d = 72 Typing this equation into the search engine and...
14. ### 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 <-- older means we add c + l = 63 <-- combined ages mean we add Substitute equation...
15. ### George has a certain number of apples, and Sarah has 4 times as many apples as George. They have a t

George has a certain number of apples, and Sarah has 4 times as many apples as George. They have a total of 25 apples. Let George's apples be g. Let Sarah's apples be s. We're give two equations: s = 4g g + s = 25 Substitute equation (1) into equation (2) for s: g + 4g = 25 If we plug this...
16. ### Ahmad has a jar containing only 5-cent and 20-cent coins. In total there are 31 coins with a total v

Ahmad has a jar containing only 5-cent and 20-cent coins. In total there are 31 coins with a total value of \$3.50. How many of each type of coin does Ahmad have? Let the number of 5-cent coins be f. Let the number of 20-cent coins be t. We're given two equations: f + t = 31 0.05f + 0.2t =...
17. ### A first number plus twice a second number is 22. Twice the first number plus the second totals 28. F

A first number plus twice a second number is 22. Twice the first number plus the second totals 28. Find the numbers. Let the first number be x. Let the second number be y. We're given two equations: x + 2y = 22 <-- Since twice means multiply by 2 2x + y = 28 <-- Since twice means multiply by...
18. ### Mark and Jennie are bowling. Jennie’s score is double Mark’s score. If the sum of their score is 171

Mark and Jennie are bowling. Jennie’s score is double Mark’s score. If the sum of their score is 171, find each person’s score by writing out an equation. Let Mark's score be m. Let Jennie's score be j. We're given two equations: j = 2m j + m = 171 Substitute equation (1) into equation (2)...
19. ### On the first day of ticket sales the school sold 3 senior citizen tickets and 10 child tickets for a

On the first day of ticket sales the school sold 3 senior citizen tickets and 10 child tickets for a total of \$82. The school took in \$67 on the second day by selling 8 senior citizen tickets And 5 child tickets. What is the price of each ticket? Let the number of child tickets be c Let the...
20. ### 5 years ago Kevin was 3 times as old as Tami. Now he is twice as old as she is. How is each now?

5 years ago Kevin was 3 times as old as Tami. Now he is twice as old as she is. How is each now? Let Kevin's age be k. Let Tami's age be t. We're given the following equations: k - 5 = 3(t - 5) k = 2t Plug equation (2) into equation (1) for k: 2t - 5 = 3(t - 5) We plug this equation into our...