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Using a system of equations, it is found that she has 9 picture books.
<h3>What is a system of equations?</h3>A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
- Variable x: Number of picture books.
- Variable y: Number of encyclopedias.
- Variable z: Number of fairy tale books.
The ratio of the number of picture books encyclopedias, and fairy tale books Annette had is 3:4:5, hence:
She gave half of her encyclopedias to her brother and he gave her 5 books of fairytales. Now she has 14 more books of fairy tales than encyclopedias, hence:
z + 5 - 0.5y = 14.
z - 0.5y = 9
From the ratios, we have that:
Hence we solve for x to find the number of picture books:
x = 9.
More can be learned about a system of equations at brainly.com/question/24342899
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