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Maru [420]
2 years ago
10

Malik and Erin run the corn harvester for Mr. Avery. Malik and Erin harvest about 2 1/3 acres' worth of corn each day. They only

have 10 1/22 days to harvest the corn. How many acres' worth of corn can they harvest for Mr. Avery?
Mathematics
1 answer:
DaniilM [7]2 years ago
8 0

Answer:

23 29/66

Step-by-step explanation:

If Malik and Erin harvest about 2 1/3 acres' worth of corn each day and they have 10 1/22 days to harvest the field, the total acres that can be harvested would be the product of 2 1/3 and 10 1/22

2\frac{1}{3} x 10\frac{1}{22}

Convert the mixed fractions to an improper fraction

\frac{7}{3} x \frac{221}{22} = \frac{1547}{66}

Convert the improper fraction back to mixed fraction To do this, divide the numerator by the denominator, the number got would be the whole number of the mixed fraction. The remainder would be the numerator

23\frac{29}{66}

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How many Solutions does this system have? (1 point)
mixas84 [53]

The given system of equation that is 2x+y=3 and 6x=9-3y has infinite number of solutions.

Option -C.

<u>Solution:</u>

Need to determine number of solution given system of equation has.

\begin{array}{l}{2 x+y=3} \\\\ {6 x=9-3 y}\end{array}

Let us first bring the equation in standard form for comparison

\begin{array}{l}{2 x+y-3=0} \\\\ {6 x+3 y-9=0}\end{array}

\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

To check how many solutions are there for system of equations a_{1} x+b_{1} y+c_{1}=0 \text{ and }a_{2} x+b_{2} y+c_{2}=0, we need to compare ratios of \frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}} \text { and } \frac{c_{1}}{c_{2}}

In our case,  

a_{1} = 2, b_{1}= 1\text{ and }c_{1}= -3

a_{2}  = 6, b_{2} = 3,\text{ and }c_{2} = -9

\begin{array}{l}{\Rightarrow \frac{a_{1}}{a_{2}}=\frac{2}{6}=\frac{1}{3}} \\\\ {\Rightarrow \frac{b_{1}}{b_{2}}=\frac{1}{3}} \\\\ {\Rightarrow \frac{c_{1}}{c_{2}}=\frac{-3}{-9}=\frac{1}{3}} \\\\ {\Rightarrow \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}=\frac{1}{3}}\end{array}

As \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}, so given system of equations have infinite number of solutions.

Hence, we can conclude that system has infinite number of solutions.

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