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"a total of around" is a grammatically correct phrase and can be used in written English.
It is commonly used to express an estimated number or quantity. Here is an example: "A total of around 50 people attended the conference."
Exact(60)
A quintet playing a total of around 30 instruments?
A total of around 40 students and faculty attended the class.
Even if Portsmouth were to enter administration, a total of around £14m would be required.
He noted that they would visit a total of around 20 in coming weeks.
About 100 employees are being dismissed there, out of a total of around 960.
Annual sales are some 50,000 copies, for a total of around 2.5 million copies to date.
In fact, a total of around 900 Chinese students are studying at the university in 2015/16.
Tragically, a total of around 2,000 people lost their lives, while more than 2 million residents were evacuated.
Local private investments created a total of around 100,000 jobs that year in both the construction sector and operation.
Since March, BlackBerry's customers have bought a total of around 17m phones, but only 5.6m have been BB10 devices.
England have a good platform for a total of around 280, which is about par I reckon.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com