Question

Georges is watering her garden, which contains red, blue and yellow flowers. If all the flowers are red except 14, and all are blue except 18, and all are yellow except 12, then how many flowers are in Georges garden?

Answer 1

Using a system of equations, it is found that 22 flowers are in George's garden.

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 red flowers.

• Variable y: Number of blue flowers.

• Variable z: Number of yellow flowers.

All the flowers are red except 14, that is, there are 14 that are blue or yellow, hence:

$y + z = 14 \rightarrow z = 14 - y$

All are blue except 18, that is, there are 18 that are red or yellow, hence:

$x + z = 18 \rightarrow z = 18 - x$

All are yellow except 12, that is, there are 12 that are red or blue, hence:

$x + y = 12 \rightarrow y = 12 - x$

From the first two equations:

$14 - y = 18 - x$

$x - y = 4$

Since $y = 12 - x$

$x - 12 + x = 4$

$2x = 16$

$x = 8$

$y = 12 - x = 12 - 8 = 4$

$z = 18 - x = 18 - 8 = 10$

The total amount of flowers in the garden is:

$x + y + z = 8 + 4 + 10 = 22$

To learn more about system of equations, you can take a look at brainly.com/question/24342899