How to solve for a , b , c , d from two equations? Need to understand how t

Eve Dunn

Eve Dunn

Answered question

2022-05-12

How to solve for a , b , c , d from two equations?
Need to understand how to solve the following question:You have 50 coins that add up to 1 dollar. What are the possible combinations of pennys, nickels, dimes, and quarters that will satisfy these limits?
P + N + D + Q = 50
.01 P + .05 N + .10 D + .25 Q = $ 1

Answer & Explanation

rynosluv101swv2s

rynosluv101swv2s

Beginner2022-05-13Added 19 answers

multiply the second equation by 100, and substract first from second. you get
4 N + 9 D + 24 Q = 50
So, for Q , you have three choises. 0, 1, or 2.
if Q = 2 then 4 N + 9 D = 2 this is impossible.
if Q = 1 then 4 N + 9 D = 26, D must be 2mod 4. trying D = 2 we get N = 2 and P = 45
if Q = 0 then 4 N + 9 D = 50. again D must be 2mod 4. trying D = 2 we get N = 8 so P = 40 . we cant choose D = 6 because then N is negative. so solution is
P N D Q 45 2 2 1 40 8 2 0

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