I AM LOST. LOST iN?

Question

Please answer the questions below, with explanation (highly needed)

1) One number is 4 less than 3 times a second number. If 3 more than twice the first number is decreased by twice the second, the result is 11. Find both numbers.

2) A Chinese problem states that several people combined their money to buy a farm tool to share. If each person paid 8 coins, they had 3 coins too many. If each paid 7 coins, they were 4 coins short. How many people were there, and what was the price in coins of the farm tool?

3) Pam sells racing team caps at her consession stand at an automobile race track.She has 100 of last year's caps and 300 of this year's caps in stock.Pam knows from past experience that her customers will pay $7 more for this year's cap than last year's.She has calculated tha she needs to make $5300 in sales of caps.Assuming thatg she will sell all caps, how much should Pam charge for each type of cap.

The solution in textbook is:

300m+100n=5300

m=n+7<- i do not understand why.

Answer 1

1)one number is 12.5 and the other is 5.5

2)there were 7 people and the tool costs 53 coins.

3)pam has to charge 8$ for old cap and 15$ for new.

    let pam charges x $ per old cap.since new caps are charged 7$ more,then for new cap charge=x+7.

then to gain 5300$.the equation is

             100x+300*(x+7)= 5300

solving above equation, you&#039;ll get x=8$.

  hence pam should charge 8$ for old and 15$ for new.