Question
Juan bought some dog food for $10 and 2 toys for x dollars each. He spent less than $25 total. How much could each toy have cost?
Write an inequality to represent the situation. Use x to represent the cost of each toy.
10+2x<25
Nice!
You just wrote an inequality to represent the situation. Now solve the associated equation, 10 + 2x = 25, to find the boundary for the inequality. Show your work or solve on paper.
10 + 2x < 25
10+2x
=
25
x
=
Write an inequality to represent the situation. Use x to represent the cost of each toy.
10+2x<25
Nice!
You just wrote an inequality to represent the situation. Now solve the associated equation, 10 + 2x = 25, to find the boundary for the inequality. Show your work or solve on paper.
10 + 2x < 25
10+2x
=
25
x
=
Answers
GPT-4o mini
To find the boundary for the inequality \(10 + 2x < 25\), we can first rewrite the corresponding equation:
\[
10 + 2x = 25
\]
Now, let's solve for \(x\):
1. Subtract 10 from both sides:
\[
2x = 25 - 10
\]
\[
2x = 15
\]
2. Divide both sides by 2:
\[
x = \frac{15}{2}
\]
\[
x = 7.5
\]
Therefore, the boundary for the inequality is \(x = 7.5\).
Now, since Juan spent less than $25 total, the cost of each toy \(x\) must be less than $7.50.
In conclusion, the cost of each toy could be:
\[
x < 7.5
\]
\[
10 + 2x = 25
\]
Now, let's solve for \(x\):
1. Subtract 10 from both sides:
\[
2x = 25 - 10
\]
\[
2x = 15
\]
2. Divide both sides by 2:
\[
x = \frac{15}{2}
\]
\[
x = 7.5
\]
Therefore, the boundary for the inequality is \(x = 7.5\).
Now, since Juan spent less than $25 total, the cost of each toy \(x\) must be less than $7.50.
In conclusion, the cost of each toy could be:
\[
x < 7.5
\]