Question
TEXTS The average number of texts sent and received per month varies for different smartphone users. Write and solve an equation to find each value.
The average 18-24 year old sends or receives 3853 texts per month. If 2022 of those texts are sent, 1 of 3.
Select Choice
are received.
The average 25-34 year old sends or receives 2240 texts per month. They send 20 more texts than they receive. They send 2 of 3.
Select Choice
texts.
The average 18-24 year old sends 360 more than twice the number of texts that an average 35-44 year old sends per month. An average 18-24 year old sends 2022 texts and an average 35-34 year old sends 3 of 3.
Select Choice
texts.
A10204_009_001A-667545.png
The average 18-24 year old sends or receives 3853 texts per month. If 2022 of those texts are sent, 1 of 3.
Select Choice
are received.
The average 25-34 year old sends or receives 2240 texts per month. They send 20 more texts than they receive. They send 2 of 3.
Select Choice
texts.
The average 18-24 year old sends 360 more than twice the number of texts that an average 35-44 year old sends per month. An average 18-24 year old sends 2022 texts and an average 35-34 year old sends 3 of 3.
Select Choice
texts.
A10204_009_001A-667545.png
Answers
GPT-4o mini
Let's break down the scenario into several parts and write equations for each part based on the information provided. We'll then solve each equation.
### Part 1: 18-24 year old texting habits
**Given**: The average 18-24 year old sends or receives a total of 3853 texts per month.
- They send 2022 texts, and the number of texts received can be calculated as:
Let \( r \) be the number of texts received.
Given:
\[ 2022 + r = 3853 \]
**Solving for \( r \)**:
\[
r = 3853 - 2022 \\
r = 1831
\]
So, an average 18-24 year old receives **1831 texts**.
### Part 2: 25-34 year old texting habits
**Given**: The average 25-34 year old sends or receives a total of 2240 texts.
- They send 20 more texts than they receive.
Let \( s \) be the number of texts sent and \( r \) the number of texts received. We know:
\[ s + r = 2240 \]
\[ s = r + 20 \]
Substituting the second equation into the first:
\[
(r + 20) + r = 2240 \\
2r + 20 = 2240 \\
2r = 2240 - 20 \\
2r = 2220 \\
r = 1110
\]
Now substituting \( r \) back into the equation for \( s \):
\[
s = r + 20 = 1110 + 20 = 1130
\]
So, an average 25-34 year old sends **1130 texts** and receives **1110 texts**.
### Part 3: Comparing age groups
**Given**: The average 18-24 year old sends 360 more than twice the number of texts that an average 35-44 year old sends per month.
- We already know an average 18-24 year old sends 2022 texts.
Let \( x \) be the number of texts that an average 35-44 year old sends.
From the problem:
\[ 2022 = 2x + 360 \]
**Solving for \( x \)**:
\[
2022 - 360 = 2x \\
1662 = 2x \\
x = \frac{1662}{2} = 831
\]
So, an average 35-44 year old sends **831 texts**.
### Summary of Results:
1. An average 18-24 year old receives **1831 texts**.
2. An average 25-34 year old sends **1130 texts**.
3. An average 35-44 year old sends **831 texts**.
### Part 1: 18-24 year old texting habits
**Given**: The average 18-24 year old sends or receives a total of 3853 texts per month.
- They send 2022 texts, and the number of texts received can be calculated as:
Let \( r \) be the number of texts received.
Given:
\[ 2022 + r = 3853 \]
**Solving for \( r \)**:
\[
r = 3853 - 2022 \\
r = 1831
\]
So, an average 18-24 year old receives **1831 texts**.
### Part 2: 25-34 year old texting habits
**Given**: The average 25-34 year old sends or receives a total of 2240 texts.
- They send 20 more texts than they receive.
Let \( s \) be the number of texts sent and \( r \) the number of texts received. We know:
\[ s + r = 2240 \]
\[ s = r + 20 \]
Substituting the second equation into the first:
\[
(r + 20) + r = 2240 \\
2r + 20 = 2240 \\
2r = 2240 - 20 \\
2r = 2220 \\
r = 1110
\]
Now substituting \( r \) back into the equation for \( s \):
\[
s = r + 20 = 1110 + 20 = 1130
\]
So, an average 25-34 year old sends **1130 texts** and receives **1110 texts**.
### Part 3: Comparing age groups
**Given**: The average 18-24 year old sends 360 more than twice the number of texts that an average 35-44 year old sends per month.
- We already know an average 18-24 year old sends 2022 texts.
Let \( x \) be the number of texts that an average 35-44 year old sends.
From the problem:
\[ 2022 = 2x + 360 \]
**Solving for \( x \)**:
\[
2022 - 360 = 2x \\
1662 = 2x \\
x = \frac{1662}{2} = 831
\]
So, an average 35-44 year old sends **831 texts**.
### Summary of Results:
1. An average 18-24 year old receives **1831 texts**.
2. An average 25-34 year old sends **1130 texts**.
3. An average 35-44 year old sends **831 texts**.