OK, I’m a little embarrassed, but my 14 yr old daughter is studying for her Grade 9 math exam this weekend and we are both stumped by one of the questions on the prep study primer the teacher gave the kids…
“Lance” has $4.35 in nickels and quarters. He has 43 coins altogether. How many nickels and quarters does Lance have?
(Show your work)
So, can one of you math whizzes bail us out?
Thanks
Brad
x = nickels
y = quarters
x + y = 43
x(.05) + y(.25) = 4.35
y= 43-x
x(.05) + y(.25) = 4.35
x (0.05) + (43 -1x) (.25) = 4.35
0.05x + 10.75 -0.25 x = 4.35
0.05x - 0.25 x = 4.35 - 10.75
-0.2 x = -6.4
x = 32
y = 43-32
y = 11
32 nickels
11 quarters
11(.25) + 32(.05)
2.75 + 1.6 = 4.35
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Sure.
X → number of quarters
Y → number of nickels
So, from your problem description we get to equations:
“Lance” has 4.35 in nickels and quarters.
1.- 0.25X + 0.05Y = 4.35
He has 43 coins altogether.
2.- X + Y = 43
so
X = (4.35 - 0.05Y) / 0.25 from 1
X = 43 - Y from 2
Since X = X then
43 - Y = (4.35 - 0.05Y) / 0.25
(0.25 * 43) - 0.25Y = 4.35-0.05Y
10.75 - 4.35 = 0.25Y - 0.05Y
6.4 = 0.20Y
0.20Y = 6.4
Y = 6.4/0.20
Y = 32
Now that we have Y, we just replace its value on equation 2
X= 43-32
X = 11
Lance has 11 quarters and 32 nickels
In case she hasn’t been taught algebra and equations yet:
If all Lance had were nickles, then he would have had 43 x 0.05 = $2.15, Now that he has 4.35 - 2.15 = $2.20 more, it means he needs 2.20 / (0.25 - 0.05) = 11 of those coins to be quarters to compensate the difference, and hence 32 are the number of nickles.
Brute force works too:
43 nickels and 0 quarters = 2.15
42 nickels and 1 quarters = 2.35
41 nickels and 2 quarters = 2.55
40 nickels and 3 quarters = 2.75
39 nickels and 4 quarters = 2.95
38 nickels and 5 quarters = 3.15
37 nickels and 6 quarters = 3.35
36 nickels and 7 quarters = 3.55
35 nickels and 8 quarters = 3.75
34 nickels and 9 quarters = 3.95
33 nickels and 10 quarters = 4.15
32 nickels and 11 quarters = 4.35
31 nickels and 12 quarters = 4.55
30 nickels and 13 quarters = 4.75
29 nickels and 14 quarters = 4.95
28 nickels and 15 quarters = 5.15
27 nickels and 16 quarters = 5.35
26 nickels and 17 quarters = 5.55
25 nickels and 18 quarters = 5.75
24 nickels and 19 quarters = 5.95
23 nickels and 20 quarters = 6.15
22 nickels and 21 quarters = 6.35
21 nickels and 22 quarters = 6.55
20 nickels and 23 quarters = 6.75
19 nickels and 24 quarters = 6.95
18 nickels and 25 quarters = 7.15
17 nickels and 26 quarters = 7.35
16 nickels and 27 quarters = 7.55
15 nickels and 28 quarters = 7.75
14 nickels and 29 quarters = 7.95
13 nickels and 30 quarters = 8.15
12 nickels and 31 quarters = 8.35
11 nickels and 32 quarters = 8.55
10 nickels and 33 quarters = 8.75
9 nickels and 34 quarters = 8.95
8 nickels and 35 quarters = 9.15
7 nickels and 36 quarters = 9.35
6 nickels and 37 quarters = 9.55
5 nickels and 38 quarters = 9.75
4 nickels and 39 quarters = 9.95
3 nickels and 40 quarters = 10.15
2 nickels and 41 quarters = 10.35
1 nickels and 42 quarters = 10.55
0 nickels and 43 quarters = 10.75
Answer: 32 nickels and 11 quarters = 4.35
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Man you got to be kidding me, I’m not smarter then a 5th Grader…LOL
Kant spell eether…lol
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LOL. That’s my usual technique, brawn over brains.
My wife, daughter and I were all stumbling around with this question and I finally said, I’m going to go on Slowtwitchand get the answer. I got a couple of blank stares. I told them “ST knows everything”.
Thanks for your help folks. ST comes thru again.
Brad
Funny. You just displayed simple numerical analysis…ie, the way a computer solves the problem.
Can I try an advanced method? Bisection method of Bolzano:
43 nickles and 0 quarters = 2.15 (A = one extreme)
0 nickles and 43 quarters = 10.75 (B = other extreme)
22 nickles and 21 quaters = 6.35 (C = mid point of AB)
33 nickles and 10 quarters = 4.15 (D = mid point of AC)
27 nickles and 16 quarters = 5.35 (E = mid point of CD)
30 nickles and 13 quarters = 4.75 (F = midpoint of DE)
31 nickles and 12 quarters = 4.55 (G = midpoint of DF)
32 nickles and 11 quarters = 4.35 (Answer = midpoint of DG)
If your computer solves problems like that, I suggest you change your OS and all the junk softwares coming with it 
You only apply brute force with a computer when there is nothing ‘smart’ to do…and even then…
Maybe I should go teach Math in HS, looks like there is work to do
Excellent.
You only apply brute force with a computer when there is nothing ‘smart’ to do…and even then…
Cut me some slack, man. I upped him with the bisection method…and even then I was still in chapter 1.
Actually in my job we use a lot of “brute force” with computers, so to speak…but yes, we use our brains as well to make sure we maximize our results. Some applications, as it stands, take a couple of days to pump out results.
I’m trying to think of how Hobbes would answer this.
Some of the strips where he is doing Calvin’s math homework are the best ones ever.
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This problem is just unrealistic: Lance has a lot more than $4.35.
If it read “After paying his lawyers, Floyd has $4.35…”, now, that would make a lot more sense.