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:
![\frac{x}{y} = \frac{3}[4}, \frac{x}{z} = \frac{3}{5}, \frac{y}{z} = \frac{4}[5}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7By%7D%20%3D%20%5Cfrac%7B3%7D%5B4%7D%2C%20%5Cfrac%7Bx%7D%7Bz%7D%20%3D%20%5Cfrac%7B3%7D%7B5%7D%2C%20%5Cfrac%7By%7D%7Bz%7D%20%3D%20%5Cfrac%7B4%7D%5B5%7D)
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](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B4%7D%7B3%7Dx%2C%20z%20%3D%20%5Cfrac%7B5%7D%7B3%7Dx)
Hence we solve for x to find the number of picture books:
![z - \frac{y}{2} = 9](https://tex.z-dn.net/?f=z%20-%20%5Cfrac%7By%7D%7B2%7D%20%3D%209)
![\frac{5}{3}x - \frac{2}{3}x = 9](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B3%7Dx%20-%20%5Cfrac%7B2%7D%7B3%7Dx%20%3D%209)
x = 9.
More can be learned about a system of equations at brainly.com/question/24342899
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Answer:
16
Step-by-step explanation:
everything simplified is 16
Answer:
C - Angle Side Angle
Step-by-step explanation:
Answer:
tăng lên 5.000 nghìn đồng
Step-by-step explanation:
mỗi chuyến bay có 0.5% hành khách mất hành lí
mỗi người đòi bồi thường 1.000.000 đồng
do đó vẽ mỗi người tăng lên :0.5%×1.000.000=5.000
Answer:
a) 0
b) 4.5
c) 3
d) 6
Step-by-step explanation:
Formula: 3x + 4y = 12
The questions contains the values of x. So here's an example of:
d) x = -4, y = ?
Using the formula: 3(-4) + 4y = 12
-12 + 4y = 12
4y = 24
y = 6
Do the same for the others!