Minor Coins
Applications Problems help?
1. Translate to an equation, then solve.
Thirteen less then five times a number is equal to 11 more than three times the number.
2. If 2 is added to a number and the sum is tripled, the result is 24 more than the number. find the number.
3. A minor league baseball team plays 98 games in a season. If the team won 14 more than twice as many games as they lost, how many wins and losses did the team have?
4. The value of an uncirculated ‘Mint State-65″ 1950 Jefferson nickel minted in Denver is 7/4 the value a 1945 nickel minted in Philadelphia in similar condition. Together the total vablue of the two coins $ 55. what is the value of each coin?
1. Let X = the number
13 Less than 5 times X is = 11 more than 3 times X
or…
5X – 13 = 11 + 3X
5X – 3X = 11 + 13
2X = 24
X = 12 — > Ans
2. Let X = the number
If 2 is + X and the sum is times 3, it is = 24 more than X
or…
3*(2 + X) = 24 + X
6 + 3X = 24 + X
3X – X = 24 – 6
2X = 18
X = 9 — > Ans.
3. Let:
X = no. of wins
Y = no. of loses
Stated in the problem is: “A minor league baseball team plays 98 games in a season.” Thus,
X + Y = 98 —> Eq.1
Stated also in the problems is: “The team won 14 more than twice as many games as they lost.”
Thus,
X = 14 + 2Y — > Eq.2
Substituting Eq.2 to Eq.1:
(14 + 2Y) + Y = 98
14 + 3Y = 98
3Y = 98 – 14
Y = 84/3 = 28 — > Substitute to Eq. 1
X + 28 = 98
X = 98 – 28 = 30
Thus,
Wins, X = 30
Losses, Y = 28
4. Let
X = Value of 1950 nickel in Denver
Y = Value of 1945 nickel in Phil
Stated in the problem is: “The value of 1950 nickel in Denver is 7/4 the value of a 1945 nickel in Philadelphia. Thus,
X = (7/4)*Y — > Eq.1
Stated also in the problem is :”The total vablue of the two coins $ 55.” Thus,
X + Y = 55 — >Eq.2
Substituting Eq.1 to Eq.2,
(7/4)*Y + Y = 55
Y*(7/4 + 1) = 55
Y*2.75 = 55
Y = 20
X = 35
That’s all about it. =)
Minor Arcana Coins an (ELV by COT)