New Ratio Calculation After Increase
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A vegetable patch has potatoes and carrots planted in it.
The ratio of potatoes to carrots is $5:2$.
There are $280$ vegetables in total.
More potatoes are planted so that the total number of potatoes increases by $10\%$.
What is the **new** ratio of potatoes to carrots in the vegetable patch?
Give your answer in its simplest form.
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Step by Step Written Solution
In this problem, we have a vegetable patch with potatoes and carrots. We're given an initial ratio and total count, and we need to find the new ratio after the number of potatoes increases. Let's start by breaking down the initial state.
Step 1: Initial Quantities
Initially, the ratio of potatoes to carrots is five to two.
We are also told the total number of vegetables is two hundred and eighty. Since the ratio is five parts to two parts, we have a total of seven parts.
To find the value of one part, we divide the total of two hundred and eighty by seven.
Now we can calculate the actual number of potatoes and carrots. Potatoes consist of five parts, so we multiply five by forty to get two hundred.
Carrots consist of two parts, so two times forty gives us eighty carrots.
Next, the problem states that the number of potatoes increases by ten percent. Let's calculate the increase first.
Step 2: Potato Increase
Ten percent of two hundred is twenty.
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