# If 𝑝 ∶ 𝑞 = 1 ∶ 2 𝑞 ∶ 𝑟 = 4 ∶ 3 𝑟 ∶ 𝑠 = 4 ∶ 5 and 𝑢 is 50% more than 𝑠, what is the ratio 𝑝 ∶ 𝑢?

If 𝑝 ∶ 𝑞 = 1 ∶ 2 𝑞 ∶ 𝑟 = 4 ∶ 3 𝑟 ∶ 𝑠 = 4 ∶ 5 and 𝑢 is 50% more than 𝑠, what is the ratio 𝑝 ∶ 𝑢?

Question: If 𝑝 ∶ 𝑞 = 1 ∶ 2 𝑞 ∶ 𝑟 = 4 ∶ 3 𝑟 ∶ 𝑠 = 4 ∶ 5 and 𝑢 is 50% more than 𝑠, what is the ratio 𝑝 ∶ 𝑢?

Solution:

Through the utilization of given ratios; the relationship between variables p, q, r and s can be established enabling us towards deducing the ratio of p:u which becomes possible after uncovering the value of variable u that is greater than s by a certain percentage.

Taking into account provided ratios such as p∶q=1∶2 leads us towards being able to develop this equation where q=2p.

After scrutinizing through q∶r =4∶3; r=(3 /4)q=(3/4)×2p =(3/2)p appears. Moreover when analyzing r ∶ 𝑠 = 4 ∶5. We determine that 𝑠 = (5 /4)𝑟 = (5 /4)×(3/2)p =(15 /8)p.

With regards to whats' stated about the relationship between variable u and s; it indicates how an increase of fifty percent greater than s occurs in its case thus making it becomes evident that

u=1.5s=1.5×(15/8)p=(45/16)p.

By dividing both sides with greatest common factor equaling to one; we establish that:

𝒎 : 𝒖 =16𝑝 :45𝑝

Thus forming a final conclusion whereupon the ratio of p∶u equates to 16 : 45.

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