Question

4) An insurance company has an initial charge to insure jewelry, plus a charge per dollar value of the jewelry. A ring with a value of $3500 costs $189.50 to insure. A ring with a value of $5900 costs $297.50 to insure. Determine the:

a. Rate of Change
b. Initial charge
c. Cost to insure a $12 000 ring
d. The value of a ring you could insure for $100


5) A school decides to sell t-shirts to raise money. If they sell 20 shirts, they will lose$30. If they sell 100 shirts, they will make $650. Determine the:
a. rate of change
b. initial value
c. number of shirts they need to sell to break even


6) Lanny got a short term job selling computers. He is paid on commission. In order to impress customers, he bought a few nice suits. If he has $20 000 in sales, he will lose $140. If he has $30 000 in sales, he will make a $90 profit. Determine the:
a. rate of change and initial value
b. the amount he needs to sell to break even
c. The amount he needs to sell in order to make $1000 profit

Answer 1

Explanation:

4) To determine the information needed, we can create a linear equation using the given data. Let's start with the rate of change, which represents the charge per dollar value of the jewelry.

To find the rate of change, we can use the formula:

Rate of Change = (Cost to insure - Initial charge) / Value of the jewelry

For the first ring:

Rate of Change = ($189.50 - Initial charge) / $3500

For the second ring:

Rate of Change = ($297.50 - Initial charge) / $5900

Since the rate of change is constant, we can equate the two expressions:

($189.50 - Initial charge) / $3500 = ($297.50 - Initial charge) / $5900

By cross-multiplying and solving for Initial charge, we can find the initial charge.

Next, to determine the cost to insure a $12,000 ring, we substitute the value of the jewelry into the linear equation we found earlier.

Similarly, to find the value of a ring that can be insured for $100, we substitute the cost into the linear equation.

5) To determine the rate of change, we can use the formula:

Rate of Change = (Profit/Loss from selling 100 shirts - Profit/Loss from selling 20 shirts) / (Number of shirts sold in 100 shirts - Number of shirts sold in 20 shirts)

To find the initial value, we need to determine the profit/loss when no shirts are sold.

To find the number of shirts needed to break even, we need to set the profit/loss equal to zero and solve for the number of shirts.

6) To determine the rate of change and initial value, we can use the formula:

Rate of Change = (Profit from $30,000 sales - Profit from $20,000 sales) / ($30,000 - $20,000)

To find the amount needed to break even, we set the profit/loss equal to zero and solve for the sales amount.

To determine the amount needed to make a $1000 profit, we can set the profit equal to $1000 and solve for the sales amount.