HELP. ALGEBRA PROBLEMS -8TH GRADE. 10PTS!?
Please and thank you guys!
1. Kevin, Dustin and Mike collect baseball cards.
- Together Dustin and Kevin have 81 cards.
- If Dustin & Mike combine their cards, they would total 96.
- The sum of Kevin's and Mike's cards is 93.
a. How many cards does each boy have
b. The boys want to store their cards in albums. The pages hold 9 cards each. How many pages will each boy need to hold his current collection.
HOW DID YOU FIND THE ANSWER?
2. Mathland High help a festival to raise money for a local charity. One of the most popular events was a dunking tank where students had a chance to dunk teachers. When Mr. B went in the booth, four students each tried to dunk him. Each one took a different number of throws before eventually hitting the target and sending Mr. B plunging into the water.
- Jorge took 1 less than twice as many throws as Shauna did
- Shauna took twice as many as Kenya did.
- Toni took two less than Jorge
-The average # of throws for the four students was 4.5. How many throws did each student take?
Jorge_____, Shauna______, Toni______, Kenya______.
THANK YOU SOO MUCH.
- 10 PTS.
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Answers & Comments
Verified answer
Here's how I'd go about the first question:
Kevin = K
Dustin = D
Mike = M
With me so far? lol
D + K = 81
D + M = 96
K + M = 93
Let's try it this way:
we need to make this one equation
D + K + D + M + K + M = 81 + 96 + 93
remember to keep the two sides of the equation separate, and whatever you do to one side of the equation, you have to do to the other.
Basic math says that a number plus a number is equal to two times that number. i.e.: M + M is equivalent to 2 x M, or more commonly, 2M
So, combine the terms on each side:
D + D + M + M + K + K = 81 + 96 + 93 or,
2D + 2M + 2K = 270
we don't have two of each boy, so let's divide each side of the equation by 2
(2D + 2M + 2K) / 2 = 270 / 2 is
D + M + K = 135
Together the boys have 135 cards
Now, start with any pair of boys, such as:
D + K = 81
We know now that
D+K+M=135 and
D+K =81, so use the substitution rule and:
81 + M = 135; cancelling the 81 from both sides yields us M and:
81 + M - 81 = 135 - 81
M = 54
and using the substitution rule, it gives us the other two dudes cards
D + 54 = 96
K + 54 = 93
cancelling gives us
96-54 = ? = D's cards
93-54 = ? = K's cards
As far as part B goes,
Divide each boys total cards by 9, and that is how many pages it will take. Anything to the right of the decimal point will mean one extra page. for example, 4.66 means 5 pages, 3.1 means 4 pages, or 10 remainder 4 equals 11 pages, etc.
Hope this helps, and I'm sorry that I don't have time to try the other equation.
Good Luck in class, and Stay in School!
--Electro--
I have the answer to #2 it is as follows: I figured it out, have not figured #1 yet....
1st 4.5 x 4 = 18 that is the total throws that the students threw average of 4.5 times the number of students (4) equals 18
Algebra formulas are as follows for each student
k = kenya
2k = Shauna
4k - 1 = Jorge
4k - 3 = Toni
11k - 4 = 18
+4 to each side, then you have
11k = 22
divide each side by 11, then you have
k = 2
Kenya = k = 2 throws
Shauna = 2k = 4 throws
Jorge = 4k - 1 = 7 throws
Toni = 4k - 3 = 5 throws
total 18 throws
when I have figured out #1 completely I will add to this comment......
I walked through Electa formulas for #1 and I agree, that is what I was working on and since they posted #1 the same way that I was going to tell you, no need to answer it twice.... So now you have the answers to both one and two.... Hope these help you...... Good luck and it was fun doing them....