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Dylan's dimes total $1.30 less than his quarters of which he has one-fourth as many as he has nickels, which total $0 more than his dimes. How many of each coin does he have?

 Jan 10, 2022
 #1
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Dylan has 4 dimes, 2 quarters, and 8 nickels.

 Jan 10, 2022
 #2
avatar+360 
+1

@ guest I think you are wrong

reason:

'Dylan's dimes total $1.30 less than his quarters "

so the quarters have to be at least 6 of them

 

My attempt:

So we need 2x as many nickels as dimes

so

quarters dimes nickels      
6 2 4 n o  
8 7 14 n o  
10 12 24 n o  
12 17 34 n o  
14 22 44 n o  
16 27 54 n o  
18 32 64 n o  
20 37 74 n o  
22 42 84 n o  
24 47 94 n o  
26 52 104 y e s
           

Thhis is acually a pretty bad method of doing it but if you noticed, there is a pattern

I'll let you find it

 Jan 10, 2022
 #3
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Yes I noticed it

quarters are adding by 2

dimes are adding by 5

nickels are adding by 10

Guest Jan 10, 2022
 #4
avatar+209 
+1

Number of nickels = x ---> cost = $0.05x

Number of quarters = x/4 ---> cost = ($0.25 * x)/4

Cost of dimes = same as of nickels = $0,05x

No. of dimes * 0.1 = 0.05x

No. of dimes = (0.05x)/0.1 = 0.5x

Also cost of dime = Cost of quarters - $1.3

0.05x = (0.25x)/4 - 1.3

=> 1.3 = 0.0125x - 0.05x

=> 1.3 = 0.0125x

=> x = 1.3/0.0125 = 104

He have 104 nickels, 104/4 = 26 quarters and 1/2 * 104 = 52 dimes

 Jan 12, 2022

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