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Word Problems/Maths Problem sum


a) John had 320 one-dollar coins and 50-cent coins in the ratio of 7:1. After his mother gave him thrice as many one-dollar coins as 50-cent coins, the ratio of one-dollar coins to 50-cent coins he had became 4:1. How many 50-cent coins did his mother give him?

b) Eric has 2/3 as many erasers as Fred. If Eric gives 8 erasers to fred, he will have 2/5 as many erasers as Fred. how many erasers does eric have at first?

(a) It is given that D + F = 320,  which means that  = 320 - F.
Since there are 7 dollars for each 50 cent piece, it is known that D/F = 7.
Since D = 320 - F, putting that into D/F = 7 gives (320-F)/F = 7.

To get the answer, multiply both sides by F, add F to both sides,
and then divide both sides by 8.
That gives 320 - F = 7F, going to 320 = 8F, an then F = 40.

Since D = 7F, and F = 40, that means D = 7*40 = 280.

Checking the answer midway gives gives the number of coins is 40 + 280 = 320, which matches.
The ratio if 280/40 = 7, which matches.

Now if we add on three dollars for every half dollar, we get a ratio of 4:1.
This means our new equation should be (280+3x)/(40+x) = 4.

Multiply this out, subtract 3x from both sides, subtract 160 from both sides, and that's it.
That is, 280 + 3x = 160 + 4x.  This goes to 120 = x.
Since we added 4 times as many dollars, that means we added 360 of them.

For dollars, we have 280+360 = 640 and for fifty cent pieces, we have 40 + 120 = 160.
Noting that 640/160 = 4, that is also seen to be correct.

(b) It is given that E = 2F/3.
It is also given that E - 8 = 2(F+8)/5.
Putting the 1st equation into the 2nd gives 2F/3 - 8 = 2(F+8)/5.
To get rid of fractions, multiply by 15.  This gives 10F - 120 = 6F + 48.

Adding 120 - 6F to both sides gives 4F = 168.
That means F = 42.
From there, using E = 2F/3, it can be seen the E = 28.

Checking the 2nd equation gives 28 - 8 = 2(42+8)/5.
That turns into 20 = 2(50)/5 = 20, so that must be right.

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Scott A Wilson


I have answered every question that was a story problems that had any relation to math for which an answer existed. I have ever answered some questions which had a vague relation to math, but still related.


My experience is from when I started doing story problems in grade school. I have been assisting, helping, and bringing smiles to many others ever since. Are you the next one?

In over 850 questions answered to other users. Maybe you're the next one ...

I received a BA in Mathematical Sciences from OSU and a MS in Mathematics from OSU as well.

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I earned Both my BS degree and MS degree with honors for having such a high grade point average.

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I have answered hundreds and hundreds of students at OSU in the 80's and over 8,500 questions right here, but only a little over 850 of them have been word problems.

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