Please expalin how to get the answer to this math problem?

Question

A gasoline company plans to mix some gasonline worth $1.45 per gallon with some worth $1.20 per gallon to make 100 gallons to sell for $1.30 per gallon. How much of each type of gasonline should be used?

Answer 1

Let's use x for the number of gallons of $1.45 gasoline and y for the number of gallons of $1.20 gasoline.

We know that x + y = 100 gallons

and that 1.45x + 1.2y = 1.3(x+y).

Now, solving this system of equations by rearranging and substitution:

x = 100-y
1.45(100-y) + 1.2y = 1.3((100-y)+y)

You should be able to do the simple algebra on your own.

Answer 2

Thisis a alligation or mixture problem . We can find the ratio in which the two quatity are mixed to get the final resultant.

Say , the first kind is A = 1.45 ( dearer)
the second kind B = 1.20 (cheaper)
the mixture M = 1.30

Now by the rule of alligation ,

ratio of A/B = (1.30 - 1.20)/ (1.45 - 1.30)
or A/B = 0.1 / 0.15 = 10/15 = 2/3

Now the total quantity is 100 Gallon , therefore

A = (2/5) *100 = 40 gallon
B = (3/5) * 100 = 60 gallon

Answer 3

let a = gallons of 1.45 gas
let b = gallons of 1.20 gas

1.45a + 1.20b = 1.30(100)
also: a+b = 100
or b = 100 - a

then: 1.45a + 1.20(100-a) = 130
1.45a + 120 - 1.20a = 130
1.45a - 1.20a = 130 - 120
.25a = 10
a = 40 gallons of 1.45 gas
and b = 100 - a
b = 100 - 40
b = 60 gallons of 1.20 gas

to check: 1.45(40) + 1.20(60) = 1.30(100)
58 + 72 = 130
130 = 130
:)

Answer 4

Ok, so we need to make 100 gallons worth 1.30 each

So we need 1.3(100) as an answer.

But, we need to add some amount of 1.20 gas to get this, we will call this x.

Also, we need to add some 1.45 gas to get this,
how much do we add?
well if we have added x already than we have 100 - x left to add to get the 100.

So,

1.20(x) + 1.45(100 - x) = 1.30(100)

1.2x + 145 - 1.45x = 130

-.25x = -15

x = 60

So, if the amount of 1.20 is 60
Then to make 100 we need 40

So 60 gallons of 1.20 and 40 gallons of 1.45

Answer 5

Let us assume that x gallons of gasoline @1.45/gallon with 100 -x gallons of gasoline @1.20/gallon is to be mixed
cost of x gallons @$1.45=$1.45x
cost of 100-x gallons@$1.20
=1.20(100-x)
=120-1.20x
Cost of 100 gallons@$1.30=$130
therefore,
1.45x+120-1.20x=130
=>1.45x-1.20x=-130-120
=> 0.25x= 10
=>x=10/0.25=40
Therefore 40 gallons @$1.45 is to be mixed with 100-40 or 60 gallons @$1.20/gallon
x= -120/-1.05

Answer 6

Cost of expensive gasoline = $1.45 * E gallons
Cost of cheap gasoline = $1.20 * C gallons
Where E + C = 100 gallons total
Cost of mixed gasoline = $1.30 * 100 gallons

Cost of expensive gasoline + Cost of cheap gasoline = Cost of mixed gasoline

(1.45 * E) + (1.20 * C) = (1.30 * 100)
(1.45 * E) + (1.20 * (100-E)) = (1.30 * 100)
(1.45 * E) + (1.20 * 100) - (1.20 * E) = (1.30 * 100)
(1.45 * E) - (1.20 * E) = (1.30 *100) - (1.20 * 100)
0.25 * E = 0.10 * 100
E = 10 / 0.25 = 40 gallons
C = 60 gallons

Answer 7

Let x = the amount of $1.45 gas
then (100 - x) = the amount of $1.20 gas
$1.45x + $1.20(100 - x) = $1.30*100
Solve for x, then (100 - x).

Answer 8

value of the final mix will be 100 gal*$1.30/gal=$130
let x=gal of $1.45 gas
x*$1.45+(100-x)*$1.20=130
1.45x+120-1.20x=130 subtract 120 from each side
1.45x-1.20x=10
0.25x=10 multiple both sides by 4
x=40
100-x=60
he will use 40 gal of $1.45/gal gas & 60 gal of $1.20/gal gas

check
40*1.45+60*1.2=58+72=$130

Answer 9

a- 1.45 X1+1.20 X2=C X
1.45 X1+1.20 X2=1.30 100
1.45 X1+1.20 X2=130 ..................................... b- X1+X2 =100 ,,,, d- 40+X2=100
c- 1.45 X1 +1.20(100-X1)=130 ,,,, X2=100-40=60gallon
1.45 X1+120 -1.20X1=130
0.25 X1=130-120=10
X1=10/0.25 =40 gallon