Miss Emily spent 5/9 of her money on 10 stuffed bears and 5 dolls. She could buy 20 stuffed bears with the rest of her money. What was the ratio of the cost of a doll to the cost of the stuffed bear?
To find the ratio of the cost of a doll to the cost of a stuffed bear, we need to know the total number of bears Miss Emily bought and the remaining number of bears she could buy.
Let's assume the total amount of money Miss Emily had was M dollars.
Given that she spent 5/9 of her money on 10 stuffed bears and 5 dolls, we can say that the cost of each stuffed bear is (5/9)M / 10 dollars and the cost of each doll is (5/9)M / 5 dollars.
She could buy 20 stuffed bears with the rest of her money, which means she has (4/9)M dollars remaining. Therefore,
The cost of each of the remaining 20 stuffed bears is (4/9)M / 20 dollars.
To find the ratio of the cost of a doll to the cost of a stuffed bear, we can compare the two values:
Ratio = Cost of a doll / Cost of a stuffed bear
Ratio = [(5/9)M / 5] / [(4/9)M / 20]
Simplifying the expression:
Ratio = [20 * (5/9)M] / [5 * (4/9)M]
Now, we can cancel out the common factors:
Ratio = 20 * 5 / 5 * 4
Ratio = 100 / 20
Ratio = 5/1
Therefore, the ratio of the cost of a doll to the cost of a stuffed bear is 5:1.
To find the ratio of the cost of a doll to the cost of a stuffed bear, we need to determine the amount of money Miss Emily spent on each item.
Let's start by assigning variables:
Let's assume the cost of a stuffed bear is "x" dollars.
And let's assume the cost of a doll is "y" dollars.
According to the information given:
Miss Emily spent 5/9 of her money on 10 stuffed bears and 5 dolls.
This means she spent 5/9 of her money on these 15 items.
We can set up an equation to represent this:
(10x + 5y) = (5/9) * Total Money
Further, we are told that she could buy 20 stuffed bears with the rest of her money. This means she spent the remaining 4/9 of her money on these 20 stuffed bears.
We can set up another equation to represent this:
20x = (4/9) * Total Money
Now we have a system of two linear equations that we can solve simultaneously to find the values of "x" and "y". Once we have the values, we can calculate the ratio of the cost of a doll to the cost of a stuffed bear by dividing the cost of the doll by the cost of the bear.
Let's solve the system of equations:
Step 1: Solve the first equation for Total Money:
(10x + 5y) = (5/9) * Total Money
Total Money = (9/5) * (10x + 5y)
Step 2: Substitute the value of Total Money in the second equation:
20x = (4/9) * (9/5) * (10x + 5y)
Step 3: Simplify the equation:
20x = (8/5) * (10x + 5y)
Step 4: Distribute:
20x = (8/5) * 10x + (8/5) * 5y
20x = 16x + 8y
Step 5: Move terms to one side:
20x - 16x = 8y
4x = 8y
Step 6: Divide both sides by 8:
x = 2y
We have found that the cost of a stuffed bear (x) is twice the cost of a doll (y). Therefore, the ratio of the cost of a doll to the cost of a stuffed bear is 1:2.
nandhan has 1 glue.marry has 25 glue.how much they have in all.
If she started with x dollars,
4/9 x = 20b
x = 45b
10b + 5d = 5/9 x
We want the ratio d/b. So,
10b + 5d = 5/9 * 45b
10b + 5d = 25b
5d = 15b
d/b = 3