Respuesta :
Andre picks 252 pounds of apples.
Further explanation:
Jane, Andre and Maria pick apples such that the apples picked by Jane are denoted by J, the apples picked by Andre are denoted by A and the apples picked by Maria are denoted by M.
The total weight of apples is 840 pounds.
Therefore, this can be written as,
[tex]{\text{J + A + M}} = 840[/tex] ...... [tex](1)\\[/tex]
Andre picks three times as many pounds Maria then .[tex]{\text{A=3M}}[/tex].
Jane picks two times pounds as Andre then .[tex]J = 2A[/tex].
Substitute 3M for A in the equation [tex]J = 2A[/tex] to obtain relation between J and M as,
[tex]\begin{aligned}{\text{J}}&={\text{2A}}\\&= {\text{2}}\cdot{\text{3M}}\\&={\text{6M}}\end{aligned}[/tex]
Now, substitute 3M for A and 6M for J in equation (1) then we get,
[tex]\begin{aligned} {\text{6M + 3M + M} &= 840}\\{\text{10M}& = 840}\\{\text{M}& = 84}\\\end {aligned}[/tex]
Therefore, Maria picks 84 pounds of apples.
Substitute the obtained value of [tex]M[/tex] as 84 in equation [tex]J = 2A[/tex] as,
[tex]\begin{gathered}{\text{J}}={\text{6}}\cdot {\text{84}}\\={\text{504}}\\\end{gathered}[/tex]
Therefore, Jane picks 504 pounds of apples.
Substitute the obtained value of [tex]M[/tex] as 84 in equation [tex]J = 6M[/tex] as,
[tex]\begin{gathered}{\text{A}}={\text{3}}\cdot {\text{84}}\\={\text{252}}\\\end{gathered}[/tex]
Therefore, Andre picks 252 pounds of apples.
Thus, the total quantity that Andre picks is [tex]\boxed{{252}\text{ } \text{pounds}}[/tex].
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Linear equations
Keywords: Linear equations, function, sets, real numbers, ordinates, abscissa, interval, open interval, closed intervals, semi-closed intervals, semi-open intervals, graph.
