The owner of Dennis's garage wants to fill a 55 gallon drum with a 20% winter mixture of antifreeze for his customers. Denis wants to mix 100% antifreeze with a 10% antifreeze mix to get a 20% mixture. How many gallons of 100% antifreeze and 10% antifreeze does he need in order to fill the drum

6.1 gallons of 100% antifreeze and 48.9 gallons of 10% antifreeze

Step-by-step explanation:

Let the amount of 100% antifreeze be x gallon

let the amount of 10% antifreeze be y gallon

total amount to drum = 55 gallons

therefore x + y = 55 Eqn 1

    100%(x) + 10(y) = 20%(55)

     x + 0.1y = 11Eqn 2

Both equations are solved simultaneously

From eqn 1 x = 55-y

Substitute x = 55-y into eqn 2

55-y+0.1y = 11

collecting like terms

44 = 0.9y

y = 48.88889

x = 55- 48.88889 = 6.11111 gallons

Therefore 6.1 gallons of 100% antifreeze and 48.9 gallons of 10% antifreeze

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

now, we can use point slope form of line

now, we can plug values

we can use point

and find b

now, we can plug it back

and we get

now, we can find revenue

we know that

revenue = price*quantity

so, we get