Question

There are 3 orchards, a, b and c. Orchard a has 60 fewer trees than orchard b orchard c has 3 times as many trees as orchard b. If the three orchards have 430 trees altogether, how many trees does orchard c have?

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Andrea

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STEP BY STEP SOLUTION:
Let's denote the number of trees in orchard b as B.
According to the information given:
1. Orchard a has 60 fewer trees than orchard b, so the number of trees in orchard a is \(B - 60\) .
2. Orchard c has 3 times as many trees as orchard b, so the number of trees in orchard c is \(3B\) .
The total number of trees in the three orchards is 430:
\[ (B - 60) + B + 3B = 430 \]
Combine like terms:
\[ 5B - 60 = 430 \]
Add 60 to both sides:
\[ 5B = 490 \]
Divide by 5:
\[ B = 98 \]
Now that we know the number of trees in orchard b (\(B = 98\)) , we can find the number of trees in orchard c:
\[ \text{Orchard c} = 3B = 3 \times 98 = 294 \]
ANSWER:
So, orchard c has 294 trees.

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