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Diano4ka-milaya [45]
3 years ago
7

A landscaper needs 348 pounds of plant food. He has 114 pounds in his truck, and another 46 pound at his shop.

Mathematics
1 answer:
Black_prince [1.1K]3 years ago
4 0

Answer:

\frac{19}{12}\ pounds

or

1\frac{7}{12}\ pounds

Step-by-step explanation:

<u><em>The correct question is </em></u>

A landscaper needs 3 4/8 pounds of plant food. He has 1 1/4 pounds in his truck, and another 4/6 pound at his shop. How many more pounds of plant food does the landscaper need?

Let

x ----> the additional pounds of plant food needed for the landscaper

we know that

The additional pounds of plant food needed for the landscaper plus the pounds in his truck plus the pounds in his shop must be equal to the total pounds of plant food needed

so

The linear equation that represent this problem is

x+1\frac{1}{4}+\frac{4}{6}=3\frac{4}{8}

Convert mixed number to an improper fractions

1\frac{1}{4}=1+\frac{1}{4}=\frac{4*1+1}{4}=\frac{5}{4}

3\frac{4}{8}=3+\frac{4}{8}=\frac{3*8+4}{8}=\frac{28}{8}=\frac{14}{4}

Substitute in the expression above

x+\frac{5}{4}+\frac{4}{6}=\frac{14}{4}

solve for x

Multiply by (4*6) both sides to remove the fractions

24x+30+16=84

Combine like terms left side

24x+46=84

subtract 46 both sides

24x=84-46

24x=38

Divide by 24 both sides

x=\frac{38}{24}\ pounds

simplify

x=\frac{19}{12}\ pounds

Convert to mixed number

\frac{19}{12}\ pounds=\frac{12}{12}+\frac{7}{12}=1\frac{7}{12}\ pounds

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