SOLUTION: The cost of a small bottle of juice is $y the cost of a large bottle of juice is $(y+1) When Jade spends $36 on small bottles only, she receives 25 more bottles than when she spe

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Question 1011333: The cost of a small bottle of juice is $y
the cost of a large bottle of juice is $(y+1)
When Jade spends $36 on small bottles only, she receives 25 more bottles than when she spends $36 on large bottles only.
(I) show that 25y^2+25y-36=0
(II) Factorise 25y^2+25y-36=0
(III) solve the equation 25y^2+25y-36=0
(IV) find the total cost of 1 small bottle of juice and 1 large bottle of juice
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
cost of a small bottle is y dollars.
cost of a large bottle is (y+1) dollars.

is the number of small bottles.
this comes from the number of small bottle times the cost of each small bottle = 36 dollars.

is the number of large bottles.
this comes from the number of large bottle times the cost of each large bottle = 36 dollars.

when she spends 36 dollars on small bottles, she has 25 more bottles than when she spends 36 dollars on large bottles.

that leads to the equation

that equation says that the number of small bottles is 25 more than the number of large bottles.

you have the equation of:

multiply both sides of that equation by y * (y+1) to get:

which becomes:

simplify to get:

subtract the left side of the equation from both sides of the equation to get:

the 36y and the -36y will cancel out when you combine like terms.

combine like terms to get:

that's the same as:

you would factorize 25y^2 + 25y - 36 to get:

(5y+9) * (5y-4) = 0

this could be done using factoring techniques or through the use of the quadratic formula.

when you solve the equation of 25y^2 + 25y - 36, you set it equal to 0 and factorize it and then solve for y.

each of the factors is set to 0 to solve for y.

5y+9 = 0 gets you y = -9/5

5y-4 = 0 gets you y = 4/5

y has to be positive so y = 4/5.

that's the cost of a small bottle.

the cost of a large bottle would be 4/5 + 1 = 9/5.

4/5 of a dollar = $0.8 dollars = 80 cents.

9/5 of a dollar = $1.8 dollars = 1 dollar and 80 cents.

the cost of a small bottle = 80 cents.
the cost of a large bottle = 1 dollar and 80 cents.

36/y = number of small bottles = 36/.8 = 45 small bottles.

36/(y+1) = 36/1.8 = 20 large bottles.

45 small bottles is 25 more than 20 large bottles.

the equation of 36/y = 36/(y+1) + 25 is good.

all of the questions have been answered.

1.
we derived 25y^2 + 25y - 36 from 36/y = 36/(y+1) + 25
2.
factors are (5y+9) * (5y-4)
3.
we got y = -9/5 and y = 4/5 where y = 4/5 was the only valid solution.
4.
the cost of a small bottle is $0.8 and the cost of a large bottle is $1.8.