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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Answer to a math 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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