Mathematics: Ezra has two weeks to sell popcorn to earn money for camp. For each unit of popcorn that he sells, Ezra will earn $5. He wants to earn at least $250 . During the first week he earned $105. How many units of popcorn must Ezra sell in the second week to earn at least $250 in the two weeks combined?

$4500Step-by-step explanation:The amount a has is 1/3 total of b, c, and d eq. 1The amount b has is 1/4 total of a, c, and d eq. 2The amount c has is 1/5 total of a, b, and d eq. 3substitute the value of in above equationsRearrange the equations to form matricesAs we knowTo find the values of matrix X, we take inverse of matrix A and multiply it with matrix BSolving using calculator yield the following resultsso,Finally, altogether they haveVerification:Lets verify if have got the right...

Ezra has two weeks to sell popcorn to earn money

Ответ:

catsareokiguess

12.03.2023

Mathematics

$4500

Step-by-step explanation:

The amount a has is 1/3 total of b, c, and d

a=1/3(b+c+d) eq. 1

The amount b has is 1/4 total of a, c, and d

b=1/4(a+c+d) eq. 2

The amount c has is 1/5 total of a, b, and d

c=1/5(a+b+d) eq. 3

d=1725

substitute the value of d=1725 in above equations

3a=b+c+1725

4b=a+c+1725

5c=a+b+1725

Rearrange the equations to form matrices

3a-b-c=1725

-a+4b-c=1725

-a-b+5c=1725

$X=\left[\begin{array}{c}a&b&c\\\end{array}\right]$

$A=\left[\begin{array}{ccc}3&-1&-1\\-1&4&-1\\-1&-1&5\end{array}\right]$

$B=\left[\begin{array}{c}1725&1725&1725\\\end{array}\right]$

As we know

AX=B

To find the values of matrix X, we take inverse of matrix A and multiply it with matrix B

$X=A^{-1} B$

$\left[\begin{array}{c}a&b&c\\\end{array}\right]=\left[\begin{array}{ccc}3&-1&-1\\-1&4&-1\\-1&-1&5\end{array}\right]^{-1} \left[\begin{array}{c}1725&1725&1725\\\end{array}\right]$