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(HURRY! ITS DUE SOON! SHOW WORK!) Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

Two students in Mr. Kelley's class, Tori and Cora, have been assigned a workbook to complete at their own pace. They get together at Tori's house after school to complete as many pages as they can. Tori has already completed 16 pages and will continue working at a rate of 5 pages per hour. Cora has completed 13 pages and can work at a rate of 8 pages per hour. Eventually, the two students will be working on the same page. How long will that take? How many pages will each of them have completed?


After _ hours, Tori and Cora will have each completed _ pages in their workbooks.

Respuesta :

kem1213
Okay, so Tori has 16 pages now, and completes 5 an hour, so her equation would look something like P=5h+16, if we let P be total pages and h be pages per hour.
Now Cora has 13 pages and does 8 per hour. So Cora’s could be P=8h+13.
Now for the substitution bit, I guess we can substitute the P in the first equation, with what P equals in the second. In other words, (P) = 5h+16 would be
8h+13 = 5h+16. Subtract 5h from both sides to get 3h+13 = 16, and subtract 13 from both sides to get 3h = 3. Now divide by three and we get h=1, or in one hour they will be the same. To get pages, just replace the h in the first equations with one (they both will have 21 pages).
I hope this answer helps! :)