Question 15:
To find out for what number of caps Company X is cheaper than Company Y, we need to set up cost equations for both companies and then set up an inequality to compare them.
Let \( n \) be the number of caps.
Cost for Company X: \[ C_X = 50 + 7n \]
Cost for Company Y: \[ C_Y = 30 + 9n \]
We want to find when Company X is cheaper than Company Y: \[ 50 + 7n < 30 + 9n \]
Now, we will solve the inequality:
- Subtract \( 7n \) from both sides: \[ 50 < 30 + 2n \]
- Subtract 30 from both sides: \[ 20 < 2n \]
- Divide both sides by 2: \[ 10 < n \]
This means that Company X is cheaper when the number of caps is more than 10 caps.
So, the answer is: More than 10 caps
Question 16:
Liz needs to maintain at least $500 in her checking account to avoid fees. She had $524.75 and wrote a check for $65.99.
First, let's calculate how much money Liz has left after writing the check:
Amount after writing the check: \[ 524.75 - 65.99 \]
Calculating that: \[ 524.75 - 65.99 = 458.76 \]
To avoid fees, Liz needs to have at least $500, so we can set up the inequality: \[ 458.76 + x \geq 500 \]
where \( x \) is the amount Liz needs to deposit.
Rearranging this gives: \[ x \geq 500 - 458.76 \] \[ x \geq 41.24 \]
The inequality that can be used to determine how much she needs to deposit into her account to avoid a fee is: \[ x \geq 41.24 \]
If you prefer a direct statement, you can say: Liz needs to deposit at least $41.24 to avoid fees.
1 answer