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1. elexusvanderhorst

2. mathstudent55

Let the number of daisies = d Let the number of roses = r Since he buys 3 more daisies than roses, you get the equation d = r + 3 The cost of each rose is \$3, so the cost of r roses is 3r The cost of each daisy is \$1, so the cost of d daisies is 1d or just d The total cost is 3r + d = 15 Solve the two equations simultaneously: d = r + 3 3r + d = 15

3. elexusvanderhorst

i dont get it

4. mathstudent55

Are you learning about systems of equations?

5. elexusvanderhorst

Using Linear Equations to Solve Problems

6. mathstudent55

Ok, let's do it with one single equation.

7. elexusvanderhorst

i dont know how to do that though

8. elexusvanderhorst

so 1+3 prety much

9. mathstudent55

No, not exactly. If the number of roses is 1, you have 1 + 3 daisies = 4 daisies. But you don't know how many roses you have, so you let the variable r stand for the number of roses. Then whatever r is, if you add 3 to it, you have the number of daisies.

10. elexusvanderhorst

i stil dont get it im sorry

11. mathstudent55

How do you represent an unknown amount in algebra? You use a variable which is a letter to represent it.

12. elexusvanderhorst

i know

13. mathstudent55

In this case, we have two things we don't know, and we are trying to find out. The two things are the number of roses and the number of daisies.

14. elexusvanderhorst

yeah

15. mathstudent55

We are given some information that allows us to find the number of roses and the number od daisies.

16. mathstudent55

One piece of information we are given is that whatever number of roses and daisies we will have, there are 3 more daisies than roses.

17. elexusvanderhorst

yes and this is so confusing

18. mathstudent55

Follow along, I'm explaining it step by step. Since we are using algebra to answer this question, and not some type of guess, we need to turn the question into an algebra problem. Algebra problems are usually solved with equations.

19. mathstudent55

In order to wrtite an equation that will help us solve this problem, we need to call some unknown numbers by letters, which are called variables in algebra.

20. mathstudent55

What are the unknown numbers we want to find? 1. The number of roses 2. The number of daisies

21. elexusvanderhorst

both

22. mathstudent55

Right. Since the word rose starts with the letter r, to make it easy to remember, I will let the letter r mean the number of roses.

23. mathstudent55

As of now, we don't know how many roses we have, but the letter r means the number of roses. We write this as: Let r = the number of roses

24. mathstudent55

We assigned the variable r to the unknown number of roses.

25. elexusvanderhorst

ok

26. mathstudent55

Now we work with thte information we are given. We are looking for two unknown numbers, the number of roses and the number of daisies. We don't know either one, but so far we have called the number of roses r. Now we need to deal with the number of daisies. We don't know that number either, but we do know something about it.

27. mathstudent55

The question states: "He buys 3 more daisies than roses". Since we are callonmg the number of roses r, and there are 3 more daisies than roses, what can we call the number of daisies? The number of roses plus 3. That is r + 3

28. mathstudent55

Now we have variables assigned to both of our unknowns: r = number of roses r + 3 = number of daisies

29. elexusvanderhorst

daisies=d

30. mathstudent55

Yes, you can call daisies d, but it won't help as much as calling daisies r + 3, since you know whatever number of roses you have, if you add 3 to it, you'll get the number of daisies.

31. elexusvanderhorst

ok sorry

32. mathstudent55

Once again, r = number of roses r + 3 = number of daisies

33. mathstudent55

Now we move on to the given information about the prices of the flowers and the total amount spent.

34. elexusvanderhorst

\$15

35. mathstudent55

The roses cost \$3 each One rose costs 1 * \$3 Two roses cost 2 * \$3 Three roses cost 3 * \$3 Four roses cost 4 * \$3 r roses cost?

36. mathstudent55

The cost of the roses is the number of roses times the cost of 1 rose. If one rose costs \$3, r roses cost r * 3 = 3r

37. mathstudent55

The same thing is true about the cost of the daisies. 1 daisy costs 1 * \$1 2 daisies cost 2 * \$1 3 daisies cost 3 * \$1 r + 3 daisies cost (r + 3)1 = r + 3

38. elexusvanderhorst

so the answer is 3 roses?

39. mathstudent55

Not yet. Now what is the total cost. You already mentioned it's \$15. The cost of the roses + the cost of the daisies = total cost The cost of the roses = 3r The cost of the daisies = r + 3 The total cost = 15 Now we can write an equation for the costs: 3r + r + 3 = 15

40. mathstudent55

Now we solve our equation: 3r + r + 3 = 15 Add the 3r and r together: 4r + 3 = 15 Subtract 3 from both sides: 4r = 12 Divide both sides by 4: r = 3 Now that we know r = 3, the number of roses is 3, since there are 3 more daisies than roses, so there are 6 daisies. The final answer is: 3 roses, 6 daisies.

41. elexusvanderhorst

ok great thank you so much

42. mathstudent55

Check: Cost of 3 roses: 3 * \$3 = \$9 Cost of 6 daisies: 6 * \$1 = \$6 Total cost: \$9 + \$6 = \$15 Total cost is correct. 6 daisies is 3 more daisies than 3 roses. Answer is correct.

43. mathstudent55

You are welcome.