Question

Leila, Abdul and Deon sent a total of 99 text messages during the weekend. Abdul sent 3 times as many messages as Deon. Leila sent 9 more messages than Deon. How many messages did they each send

Answer 1

Let,

x = number of texts Leila sent

y = number of texts Abdul sent

z = number of texts Deon sent

Let's generate equations based on the given relationships.

a.) Abdul sent 3times as many messages as Deon.

$\text{ y = 3z}$

b.) Leila sent 9 more messages than Deon.

$\text{ x = z + 9}$

c.) Leila, Abdul and Deon sent a total of 99 text messages during the weekend.

$\text{ x + y + z = 99}$

Step 1: Let's determine the number of texts that Deon sent.

$\text{ x + y + z = 99}$$\text{ x + (3z) + (z + 9) = 99}$$\text{ x + 3z + z + 9 = 99}$$\text{ 5z + 9 = 99}$$\text{ 5z = 99 - 9}$$\text{ 5z = 90}$$\text{ }\frac{\text{5z}}{\text{ 5}}\text{ = }\frac{\text{90}}{\text{ 5}}$$\text{ z = 18 = 18 text messages}$

Therefore, Deon sent 18 text messages.

For Abdul:

y = 3z

y = 3(18)

y = 54

Therefore, Abdul sent 54 text messages.

For Leila:

x = z + 9

x = 18 + 9

x = 27

Therefore, Leila sent 27 text messages.