Question

The ratio of the number of picture books encyclopedias, and fairy tale books Annette had is 3:4:5 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 How many picture books does she have?

Answer 1

Using a system of equations, it is found that she has 9 picture books.

What is a system of equations?

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:

$\frac{x}{y} = \frac{3}[4}, \frac{x}{z} = \frac{3}{5}, \frac{y}{z} = \frac{4}[5}$

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:

$y = \frac{4}{3}x, z = \frac{5}{3}x$

Hence we solve for x to find the number of picture books:

$z - \frac{y}{2} = 9$

$\frac{5}{3}x - \frac{2}{3}x = 9$

x = 9.

More can be learned about a system of equations at brainly.com/question/24342899

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