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# simultaneous equations

1. ### JP's age is twice the age of Reyna. The sum of their ages does not exceed 51

JP's age is twice the age of Reyna. The sum of their ages does not exceed 51 Let JP's age be j. Let Reyna's age be r. We're given two expressions: w = 2r r + w <= 51. (Does not exceed means less than or equal to) We substitute (1) into (2) for w to get the inequality: r + 2r <= 51 To solve...
2. ### A used book store also started selling used CDs and videos. In the first week, the store sold a comb

A used book store also started selling used CDs and videos. In the first week, the store sold a combination of 40 CDs and videos. They charged \$4 per CD and \$6 per video and the total sales were \$180. Determine the total number of CDs and videos sold. Let the number of cd's be c and number of...
3. ### April, May and June have 90 sweets between them. May has three-quarters of the number of sweets that

April, May and June have 90 sweets between them. May has three-quarters of the number of sweets that June has. April has two-thirds of the number of sweets that May has. How many sweets does June have? Let the April sweets be a. Let the May sweets be m. Let the June sweets be j. We're given...
4. ### Rigby and Eleanor's combined score on the systems of equations test was 181. Rigby scored 9 more poi

Rigby and Eleanor's combined score on the systems of equations test was 181. Rigby scored 9 more points than Eleanor. What were Eleanor and Rigby's scores? Let Rigby's score be r Let Eleanor's score be e We're given two equations: r = e + 9 e + r = 181 Substitute equation (1) into equation...
5. ### The fraction has a value of 3/5. The sum of the numerator and the denominator was 40. What was the f

The fraction has a value of 3/5. The sum of the numerator and the denominator was 40. What was the fraction? We're given two equations with a fraction with numerator (n) and denominator (d): n + d = 40 n/d = 3/5 Cross multiply equation 2, we get: 5n = 3d Divide each side by 5: 5n/5 = 3d/5 n...
6. ### Megan has \$50 and saves \$5.50 each week. Connor has \$18.50 and saves \$7.75 each week. After how many

Megan has \$50 and saves \$5.50 each week. Connor has \$18.50 and saves \$7.75 each week. After how many weeks will megan and connor have saved the same amount Set up the Balance function B(w) where w is the number of weeks for Megan: B(w) = savings per week * w + Current Balance B(w) = 5.50w + 50...
7. ### Sadie and Connor both play soccer. Connor scored 2 times as many goals as Sadie. Together they score

Sadie and Connor both play soccer. Connor scored 2 times as many goals as Sadie. Together they scored 9 goals. Could Sadie have scored 4 goals? Why or why not? Assumptions: Let Connor's goals be c Let Sadie's goals be s We're given the following simultaneous equations: c = 2s c + s = 9 We...
8. ### The school is selling potted plants as a fundraiser. Kara sold 12 ferns and 8 ivy plants for 260.00.

The school is selling potted plants as a fundraiser. Kara sold 12 ferns and 8 ivy plants for 260.00. Paul sold 15 ivy plants and 6 ferns for 240. What’s the selling price of each plant. Let the cost of each fern be f Let the cost of each ivy plant be I We're given: 12f + 8i = 260 15i + 6f =...
9. ### The first group orders 3 pizzas and 4 drinks for \$33.50. The second group orders 5 pizzas and 6 drin

The first group orders 3 pizzas and 4 drinks for \$33.50. The second group orders 5 pizzas and 6 drinks for \$54. Find the cost for each pizza and each drink Assumptions: Let the cost of each pizza be p Let the cost of each drink be d Givens: 4d + 3p = 33.50 6d + 5p = 54 We have a...
10. ### An orchard has 378 orange trees. The number of rows exceeds the number of trees per row by 3. How ma

An orchard has 378 orange trees. The number of rows exceeds the number of trees per row by 3. How many trees are there in each row? We have r rows and t trees per row. We're give two equations: rt = 378 r = t + 3 Substitute equation (2) into equation (1) for r: (t + 3)t = 378 Multiply...
11. ### A motorboat travels 408 kilometers in 8 hours going upstream and 546 kilometers in 6 hours going dow

A motorboat travels 408 kilometers in 8 hours going upstream and 546 kilometers in 6 hours going downstream. What is the rate of the boat in still water and what is the rate of the current? Assumptions: B = the speed of the boat in still water. S = the speed of the stream Relative to the...
12. ### A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every

A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every black marble. How many red marbles are in the bag? Let the red marbles be r Let the black marbles be b. A 19 to 1 red to black is written as: r = 19b We're also given: b + r = 120 Substitute r...
13. ### 508 people are there, the daily price is \$1.25 for kids and \$2.00 for adults. The receipts totaled \$

508 people are there, the daily price is \$1.25 for kids and \$2.00 for adults. The receipts totaled \$885.50. How many kids and how many adults were there? Assumptions: Let the number of adults be a Let the number of kids be k Given with assumptions: a + k = 508 2a + 1.25k = 885.50 (since...
14. ### She earns \$20 per hour as a carpenter and \$25 per hour as a blacksmith, last week Giselle worked bot

She earns \$20 per hour as a carpenter and \$25 per hour as a blacksmith, last week Giselle worked both jobs for a total of 30 hours, and a total of \$690. How long did Giselle work as a carpenter and how long did she work as a blacksmith? Assumptions: Let b be the number of hours Giselle worked...
15. ### In an algebra test, the highest grade was 50 points higher than the lowest grade. The sum of the two

In an algebra test, the highest grade was 50 points higher than the lowest grade. The sum of the two grades was 180. Let the high grade be h and the low grade be l. We're given: h = l + 50 h + l = 180 Substitute equation (1) into equation (2) for h l + 50 + l = 180 To solve this equation, we...
16. ### At a concert there were 25 more women than men. The total number of people at the concert was 139. F

At a concert there were 25 more women than men. The total number of people at the concert was 139. Find the number of women and the number of men at the concert. Let men be m and women be w. We're given two equations. w = m + 25 m + w = 139 Substitute equation (1) into equation (2): m + m +...
17. ### A 12% acid solution is made by mixing 8% and 20% solutions. If the 450 ml of the 12% solution is req

A 12% acid solution is made by mixing 8% and 20% solutions. If the 450 ml of the 12% solution is required, how much of each solution is required? Component Unit Amount 8% Solution: 0.08 * x = 0.08x 20% Solution: 0.2 * y = 0.2y 12% Solution: 0.12 * 450 = 54 We add up the 8% solution and 20%...
18. ### If Quinn has 4 times as many quarters as nickels and they have a combined value of 525 cents, how ma

If Quinn has 4 times as many quarters as nickels and they have a combined value of 525 cents, how many of each coin does he have? Using q for quarters and n for nickels, and using 525 cents as \$5.25, we're given two equations: q = 4n 0.25q + 0.05n = 5.25 Substitute equation (1) into equation...
19. ### a boy purchased a party-length sandwich 57 inches long. he wants to cut it into three pieces so that

a boy purchased a party-length sandwich 57 inches long. he wants to cut it into three pieces so that the middle piece is 6inches longer than the shortest piece and the shortest piece is 9 inches shorter than the longest price. how long should the three pieces be? Let the longest piece be l. The...
20. ### A house painting company charges \$376 plus \$12 per hour. Another painting company charges \$280 plus

A house painting company charges \$376 plus \$12 per hour. Another painting company charges \$280 plus \$15 per hour. How long is a job for which both companies will charge the same amount? Set up the cost function for the first company C(h) where h is the number of hours: C(h) = Hourly Rate * h +...