Dave and Ellen are newly married and living in their first house. The yearly premium on their homeowner's insurance policy is $450 for the coverage they need. Their insurance company offers a 5 percent discount if they install dead-bolt locks on all exterior doors. The couple can also receive a 2 percent discount if they install smoke detectors on each floor. They have contacted a locksmith, who will provide and install dead-bolt locks on the two exterior doors for $50 each. At the local hardware store, smoke detectors cost $7 each, and the new house has two floors. Dave and Ellen can install them themselves.

A. 4.44years

B. 1.5years

C. Yes

Step-by-step explanation:

a. Calculation to determine how many years will it take Dave and Ellen to earn back in discounts the cost of the dead-bolts

First step is to determine the Annual discount for dead-bolts using this formula

Annual discount for dead-bolts=Discount percent × Annual premium

Let plug in the formula

Annual discount for dead-bolts=0.05 × $450

Annual discount for dead-bolts=$22.50

Now let determine the Recovery period using this formula

Recovery period=Cost of dead-bolts / Annual discount for dead-bolts

Let plug in the formula

Recovery period= (2 × $50)/ $22.50

Recovery period=$100/$22.50

Recovery period= 4.44years

Therefore Assuming their insurance rates remain the same, how many years will it take Dave and Ellen to earn back in discounts the cost of the dead-bolts will be 4.44years

b. Calculation to determine How many years will it take Dave and Ellen to earn back in discounts the cost of the smoke detectors

First step is to calculate the Annual discount for smoke alarms using this formula

Annual discount for smoke alarms=Discount percent × Annual premium

Let plug in the formula

Annual discount for smoke alarms=0.02 × $450

Annual discount for smoke alarms=$9.00

Now let determine the Recovery period using this formula

Recovery period=Cost of smoke alarms / Annual discount for smoke alarms

Let plug in the formula

Recovery period=(2 × $7) / $9.00

Recovery period=$14/$9.00

Recovery period= 1.5 years

Therefore How many years will it take Dave and Ellen to earn back in discounts the cost of the smoke detectors will be 1.5years

C. YES, Based on the information I WOULD recommend Dave and Ellen to invest in the SAFETY ITEMS, if they plan to stay in that house for about 5 years reason been that a home that is equipped with HOME SAFETY ITEMS can help to prevent UNFORESEEABLE ACCIDENTS that may occur, which is why SAFETY ITEMS is vital for every home regardless of the recovery period.

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!