David weighs 5 kg less than John. Who in turn is 8 kg lighter than Paul If their total weight is 197 kg. How heavy is each person?

Answer 1

for this question, you just have to give one of the guys a variable. once you figure out what he is, you can do simple math to figure out the rest of their weights : here i am going to use P as the variable to represent Paul's weight. what is written in bold is the procedure you would write. i just explained it along the way in brackets

Let P represent Pauls total weight

let (p-8) represent Johns total weight ( because John is 8 kg lighter than Paul, so pauls weight minus 8 kg must be Johns weight)

let (p-8)-5 represent Davids weight (David is 5 kg lighter than John, so if John is (p-8), then David must be (p-8)-5)

(if all of their weights together is 197, then:

P+(P-8)+(P-8)-5=197

(get rid of the brackets because there is a plus sign between them, so you cannot expand by multiplying)

P+P-8+P-8-5=197

(collect the like terms, in this case P on one side of the equal sign and the numbers on the other side)

P+P+P=197+8+8+5 (when moving a number to the other side, you need to change the sign from negative to positive in this case)

3P=218 (P+P+P=3p and then add the numbers to get 218)

3P/3=218/3 (divide both sides by 3, because you want to isolate only P, and not have 3P)

P=72.6

(Now you have pauls weight, so you can just do simple math to figure out the others weights)

therefore, Pauls weight is 72.6 kg (you can round up if you want, but for more accurate answer's, i didnt)

If Johns weight is (P-8), then his weight is 72.6-8 =64.6. therefore johns weight is 64.6 kg

If Davids weight is Johns weight -5, then his weight is 64.6-5=59.6 kg

(Now you can add up all the weights to check and see if it meets 197)

59.6+64.6+72.6=196.8 (since you are working with a decimal number, this is the best you will get. if you rounded up, then you will have a bigger number than 197. 196.8 can be rounded final answer to 197)

hope this helped:)