Math / Algebra

Question4.) Leo spent less than $\$ 50$ on pizza for friends. He purchased 4 large pizzas. He says the cost of each pizza, p, in dollars, can be represented by the inequality statement $4 p<50$ . What is the solution to this inequality and what does it mean in that context? a) The solution is $p=12.5$ and it means each pizza costs $\$ 12.50$ . b) The solution is $p<12.5$ and it means each pizza costs less than \ $12.50. c) The solution is$ p>12.5 $and it means each pizza costs more than \$12.50. d) The solution is$ p<46 $and it means each pizza costs less than$ \ $46$ .

Studdy Solution

STEP 1

What is this asking? If Leo bought 4 pizzas for less than $\$50$ , how much did each pizza cost? Watch out! Don't forget that we're looking for the price per pizza, not the total cost!
Also, remember to keep the inequality sign correct.

STEP 2

1. Set up the inequality.
2. Solve for $p$ .
3. Interpret the solution.

STEP 3

We know that Leo spent less than $\$50$ on 4 pizzas.
Let's use $p$ to represent the price of each pizza.
Since he bought 4 pizzas, the total cost is $4 \cdot p$ , or $4p$ .
We're told this total cost is less than $\$50$ , so our inequality is $4p < 50$ .

STEP 4

To find the maximum price of each pizza, we need to isolate $p$ .
Our inequality is $4p < 50$ .
We want to get $p$ by itself, so we need to turn the $4p$ into $1p$ .
We can do this by dividing both sides of the inequality by 4.
Remember, what we do to one side, we must do to the other to keep things balanced!

STEP 5

Dividing both sides by 4, we get: $\frac{4p}{4} < \frac{50}{4}$ $p < \frac{50}{4}$

STEP 6

Now, let's simplify the right side: $\frac{50}{4} = \frac{25 \cdot 2}{2 \cdot 2} = \frac{25}{2} \cdot \frac{2}{2} = \frac{25}{2} \cdot 1 = \frac{25}{2} = 12.5$ So, $p < 12.5$ .

STEP 7

Our solution, $p < 12.5$ , means that the price of each pizza ( $p$ ) is less than $\$12.50$ .
This makes sense because Leo spent less than $\$50$ on 4 pizzas.

STEP 8

The solution is $p < 12.5$ , which means each pizza costs less than $\$12.50$ .
This corresponds to answer choice (b).

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Studdy Solution

STEP 1

What is this asking? If Leo bought 4 pizzas for less than $\$50$ , how much did each pizza cost? Watch out! Don't forget that we're looking for the price per pizza, not the total cost!
Also, remember to keep the inequality sign correct.

STEP 2

1. Set up the inequality.
2. Solve for $p$ .
3. Interpret the solution.

STEP 3

We know that Leo spent less than $\$50$ on 4 pizzas.
Let's use $p$ to represent the price of each pizza.
Since he bought 4 pizzas, the total cost is $4 \cdot p$ , or $4p$ .
We're told this total cost is less than $\$50$ , so our inequality is $4p < 50$ .

STEP 4

STEP 5

Dividing both sides by 4, we get: $\frac{4p}{4} < \frac{50}{4}$ $p < \frac{50}{4}$

STEP 6

Now, let's simplify the right side: $\frac{50}{4} = \frac{25 \cdot 2}{2 \cdot 2} = \frac{25}{2} \cdot \frac{2}{2} = \frac{25}{2} \cdot 1 = \frac{25}{2} = 12.5$ So, $p < 12.5$ .

STEP 7

Our solution, $p < 12.5$ , means that the price of each pizza ( $p$ ) is less than $\$12.50$ .
This makes sense because Leo spent less than $\$50$ on 4 pizzas.

STEP 8

The solution is $p < 12.5$ , which means each pizza costs less than $\$12.50$ .
This corresponds to answer choice (b).

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Studdy Solution

STEP 1

What is this asking? If Leo bought 4 pizzas for less than $50\$50$50, how much did each pizza cost? Watch out! Don't forget that we're looking for the price *per pizza*, not the total cost!Also, remember to keep the inequality sign correct.

STEP 2

1. Set up the inequality.2. Solve for ppp.3. Interpret the solution.

STEP 3

We know that Leo spent less than $50\$50$50 on 4 pizzas.Let's use ppp to represent the price of each pizza.Since he bought 4 pizzas, the **total cost** is 4⋅p4 \cdot p4⋅p, or 4p4p4p.We're told this total cost is less than $50\$50$50, so our inequality is 4p<504p < 504p<50.

STEP 4

STEP 5

Dividing both sides by **4**, we get: 4p4<504 \frac{4p}{4} < \frac{50}{4} 44p​<450​ p<504 p < \frac{50}{4} p<450​

STEP 6

Now, let's simplify the right side: 504=25⋅22⋅2=252⋅22=252⋅1=252=12.5 \frac{50}{4} = \frac{25 \cdot 2}{2 \cdot 2} = \frac{25}{2} \cdot \frac{2}{2} = \frac{25}{2} \cdot 1 = \frac{25}{2} = 12.5 450​=2⋅225⋅2​=225​⋅22​=225​⋅1=225​=12.5 So, p<12.5p < 12.5p<12.5.

STEP 7

Our solution, p<12.5p < 12.5p<12.5, means that the price of each pizza (ppp) is *less than* $12.50\$12.50$12.50.This makes sense because Leo spent *less than* $50\$50$50 on 4 pizzas.

STEP 8

The solution is p<12.5p < 12.5p<12.5, which means each pizza costs less than $12.50\$12.50$12.50.This corresponds to answer choice (b).

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What is this asking? If Leo bought 4 pizzas for less than $\$50$ , how much did each pizza cost? Watch out! Don't forget that we're looking for the price per pizza, not the total cost!
Also, remember to keep the inequality sign correct.

1. Set up the inequality.
2. Solve for $p$ .
3. Interpret the solution.

We know that Leo spent less than $\$50$ on 4 pizzas.
Let's use $p$ to represent the price of each pizza.
Since he bought 4 pizzas, the total cost is $4 \cdot p$ , or $4p$ .
We're told this total cost is less than $\$50$ , so our inequality is $4p < 50$ .

Dividing both sides by 4, we get: $\frac{4p}{4} < \frac{50}{4}$ $p < \frac{50}{4}$

Now, let's simplify the right side: $\frac{50}{4} = \frac{25 \cdot 2}{2 \cdot 2} = \frac{25}{2} \cdot \frac{2}{2} = \frac{25}{2} \cdot 1 = \frac{25}{2} = 12.5$ So, $p < 12.5$ .

Our solution, $p < 12.5$ , means that the price of each pizza ( $p$ ) is less than $\$12.50$ .
This makes sense because Leo spent less than $\$50$ on 4 pizzas.

The solution is $p < 12.5$ , which means each pizza costs less than $\$12.50$ .
This corresponds to answer choice (b).