Our teachers are having a toy drive. Mrs. A collected 10 more toys than Mr. B. Mrs. C collected twice as many toys as Mr. B. Mr. D collected 3 less than Mrs. C. Mrs. E collected 50 more than Mrs. A. Together they collected 487 toys in all and gave them to another teacher. How many toys did each teacher collect. I have to show how I did this with a full explanation.
Let x equal the number of toys Mr. B. collected.
Then, x+10 will equal the number of toys Mrs. A collected, as she collected 10 more than B.
And, 2x will equal the number of toys Mrs. C collected, as she collected twice what B collected.
As a result of the above three items, we then know that 2x-3 is the number of toys Mr. D collected, as he collected three less than Mrs. C.
Finally, x+10+50 = x+60 will equal the number of toys Mr. E collected, given that he collected 50 more than Mrs. A, who collected x+10.
Since they collected 487 toys total, we find out how many toys each teacher collected by the equation:
x + (x + 10) + (2x) + (2x - 3) + (x+60) = 487.
=> 7x + 67 = 487
=> 7x = 427
=> x = 61 which is the number of toys Mr. B collected.
From this we can work backwards to find the rest of the teachers.
Hope that helps =)
Thank you.
To solve this problem, we need to use logical thinking and basic algebra skills. Let's break down the information given and determine the number of toys collected by each teacher step by step:
Step 1: Assign variables to the unknown quantities:
Let's assume the number of toys collected by Mr. B is "x". We can then express the number of toys collected by other teachers in terms of "x".
Step 2: Use the given information to write equations:
- Mrs. A collected 10 more toys than Mr. B, so the number of toys she collected is (x + 10).
- Mrs. C collected twice as many toys as Mr. B, so the number of toys she collected is 2x.
- Mr. D collected 3 less than Mrs. C, so the number of toys he collected is (2x - 3).
- Mrs. E collected 50 more than Mrs. A, so the number of toys she collected is [(x + 10) + 50] or (x + 60).
Step 3: Combine the equations and set up the total equation:
To find the total number of toys collected, we add up the number of toys collected by each teacher:
(x) + (x + 10) + (2x) + (2x - 3) + (x + 60) = 487
Step 4: Solve the equation:
Combine like terms:
7x + 67 = 487
Subtract 67 from both sides:
7x = 420
Divide both sides by 7:
x = 60
Step 5: Find the number of toys collected by each teacher:
- Mr. B collected 60 toys.
- Mrs. A collected (60 + 10) = 70 toys.
- Mrs. C collected 2 * 60 = 120 toys.
- Mr. D collected (2 * 60) - 3 = 117 toys.
- Mrs. E collected (70 + 50) = 120 toys.
Therefore, Mr. B collected 60 toys, Mrs. A collected 70 toys, Mrs. C collected 120 toys, Mr. D collected 117 toys, and Mrs. E collected 120 toys.