# A farmer has 3/5 of his land under cultivation, 3/4 of which is in soy beans. How much land does the farmer have if he has 270 acres of soy beans?

Oct 30, 2015

$121 \frac{1}{2} \text{ acres}$

#### Explanation:

Let total amount of land be${L}_{t}$
Let land cultivated be ${L}_{c}$
Let land for soy beans be ${L}_{s}$

so ${L}_{c} = \frac{3}{5} {L}_{t}$ ..................................(1)
so ${L}_{s} = \frac{3}{4} {L}_{c}$..................................(2)

Substitute (1) into (2) giving:

${L}_{s} = \frac{3}{4} \times \frac{3}{5} \times {L}_{t}$ ..............(3)

Given that ${L}_{s} = 270 \text{ acres}$
Substitution into (3) gives:

$270 \text{ acres" = 3/4 times 3/5 times L_t " acres}$

Thus
${L}_{t} = 270 \times \frac{9}{20}$

$L t = 121 \frac{1}{2}$ acres

Tip: question given in fractions so answer given in fractions.
Do not forget the units. That is a bad and very common mistake!

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