Let cost of Emma's phone = x
Given that cost of Sophie's phone = 640
Then ratio of their phones cost will be x:640 or x/640
Given that ratio of their phones cost is 7:8 or 7/8
So both ratios will be equal.
[tex]\frac{x}{640}=\frac{7}{8}[/tex]
[tex]x=\frac{7}{8}*640[/tex]
x=560
So the new ratio of the cost of their phones will be 560:640
Now we have to find about how much should the prices of their phones decrease in order to have a ratio of 9:11.
So let that decreased amount is k then we will get equation :
[tex]\frac{560-k}{640-k}=\frac{9}{11}[/tex]
11(560-k)=9(640-k)
6160-11k=5760-9k
6160-5760=11k-9k
400=2k
200=k
Hence final answer is prices of their phones should decrease by 200 in order to have a ratio of 9:11.
Answer:
For the ratio between the price of the phones to be 9:11, the price of Emma's phone must decrease from $ 560 to $ 523.66. That is, the price of Emma's phone should decrease $ 36,364
Step-by-step explanation:
To answer this question, call x on Emma's phone and z on Sophie's phone.
We know that the price relationship between x and z is 7: 8
This means that:
[tex]\frac{7}{8} =\frac{x}{z}[/tex]
We know that the price of Sophie's phone is $ 640
Entoces z = 640
Now we clear x
[tex]\frac{7}{8} =\frac{x}{640}\\ x =640}\frac{7}{8}=560\\ x = 560[/tex]
Then, if the new relationship is 9:11 then:
[tex]\frac{9}{11} =\frac{x}{640}[/tex]
x = $523,636
For the ratio between the price of the phones to be 9:11, the price of Emma's phone must decrease from $ 560 to $ 523.66. That is, the price of Emma's phone should decrease $ 36,364
