Question

Henrietta decides to learn 768 new magic spells before her final exam. She plans to learn the same number each day. In the first 5 days, she learns exactly the number of spells she planned to learn. In the remaining days before her exam, Henrietta learns 6 more spells each day than planned. When she still had 1 day left before her exam, Henrietta calculated that she learned 844 new magic spells. How many magic spells did Henrietta plan to learn each day?

Answer 1

Answer:

32 days

Step-by-step explanation:

make a rate time distance chart:

                   r             t         d

first 5         | y  |     5        | 5y

final days | y+6 | x-6        | (y+6)(x-6)

take y for planned rate and x for time till test

then make system of equations:

1. 5y+(y+6)(x-6) = 844

2. 768/y =x

/Henrietta knew the time till test, so we can assume that she planned in such a way that would mean she learned exactly 768 spells if she worked at the set rate. On this assumption we make 2

solve, and you get 2 options: x=-10/3 y =-144 (exclude, negative)

the second one is x=24 y=32 that works for us, so answer is she planned to learn 32 spells each day.

Answer 2

The number of magic Henrietta planned to learn each day is 32

Represent the number of magic learned each day in the first 5 days with x, and the total days with y.

So, the total number of magic learned in this time frame is:

Total = 5x

In the remaining days (i.e y - 5), she learned 6 more each day

i.e. x + 6

So, the total number of magic learned in this remaining days is:

Total = (x + 6)(y - 5)

So, we have the following system of equations:

$5y+(x+6)(y-5) = 844$

$xy = 768$

Using a graphing calculator, we have:

(x,y) = (32, 24)

Hence, the number of magic she planned to learn each day is 32

Read more about system of equations at:

https://brainly.com/question/14323743