Posted by Brandon on .
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 =)