Question

The solution for which of the following requires use of absolute value?

a: At a school fundraiser, students washed twenty cars for 5$ per vehicle. Each driver donated and additional $3-$5. How much money was raised.
b: A local merchant donates 10% of her sales on the first day of each month to a local cause. if her annual donations total $1500 what is her average daily sales?
c: If gas cost $3.50 per gallon, how much did Celia pay to fill her tank with 8.2 gallons?
d: Marissa ran a half marathon (about 13.1 miles) in 2 hours and 4 minutes. what was her speed?

Answer 1

Answers
a). Minimum =$160
Maximum =$200
b). $410.96
c). $28.7
d). 0.105645161 miles per minute.

Explanation a.
For the first statements (a) there would be no absolute value. It is a range.
There are 20 vehicles, each washed at $5.
$5×20=$100
If there are 20 vehicles then there are 20 drivers.
$3×20=$60 or $5×20=#100
Total amount of money raised
(60+100) to (100+100)
Minimum =$160
Maximum =$200

Explanation b
Let x be her daily sales. There are 365 days in one year.
Donation for one day = 10% of x = 0.01x
Donation for 1 year =0.01x×365=3.65x
3.65x=1500
x=410.96
Donation for 1 day = $410.96

Explanation c.
Cost of 1 gallon = $3.50
Cost of 8.2 gallon = $3.50×8.2=$28.7

Explanation d.
Marissa runs 13.1 miles in 2 hours and 4 minutes
That is to say that she runs 13.1 miles in ((2×60)+4) minutes.
((2×60)+4)=124 minutes.
speed=distance/(time taken)
speed=13.1/124=0.105645161 miles per minute.

Answer 2

Part a) At a school fundraiser, students washed twenty cars for 5$ per vehicle. Each driver donated and additional $3-$5. How much money was raised.

we know that

raised money=total vehicle*[$5+absolute value($3-$5)]
raised money=20*[$5+absolute value(-2)]
raised money=20*[$7]
raised money=$140
the answer Part a) is $140

Part b)A local merchant donates 10% of her sales on the first day of each month to a local cause. if her annual donations total $1500 what is her average daily sales?

step 1
divide $1500 by 12
1500/12=$125/month

if $125 is ------------> 10%
x------------------> 100%
x=100*125/10-----> x=$1250

the answer Part b) is $1250

Part c)If gas cost $3.50 per gallon, how much did Celia pay to fill her tank with 8.2 gallons?

multiply $3.50 by 8.2 gallons
3.5*8.2=$28.7

the answer Part c) is $28.7

Part d) Marissa ran a half marathon (about 13.1 miles) in 2 hours and 4 minutes. what was her speed?

we know that
speed=distance /time
distance=13.1 miles
time=2 hours and 4 minutes----> 2+(4/60)---> 2.07 hour
time=2 hours and 4 minutes----> 2*60+(4)---> 124 minutes
speed=13.1/2.07----> 6.33 miles/hour
speed=13.1/124----> 0.106 miles/minutes

the answer part d) is 6.33 miles/hour or 0.106 miles/minutes



The solution to problem a) requires the use of absolute value