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The phrase "a balance of" is correct and can be used in written English.
Generally, the phrase is used to refer to a combination or equilibrium of two or more things. For example, "We need to find a balance of power between the two countries."
Exact(54)
There's a balance of both genders.
A balance of power leads to conflict.
A balance of skills.
That leaves a balance of $18 billion.
One case, a balance of judgments.
A balance of education and enforcement.
Similar(6)
"Only a balance of fear will preserve peace.
It implies equilibrium-a balance of power.
"It's a balance-of-power issue".
Some states, like Tennessee, take a balance-of-interests approach.
Chatter spread of a balance-of-payments problem.
More suggestions(21)
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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