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Kelsie Sawayn

Feb 20, 2025

A four-digit integer, WXYZ, in which W,X,Y and Z each represent a different digit, is formed according to the?

following rules X=W+Y+Z2.W=Y+13.Z=W-5
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4 Answers

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Hermina Ferry

Feb 20, 2025

W is the key variableZ = W-5Y = W-1X = W+Y+Z = W+(W-1)+ (W-5) = 3W-6This means:W can't be less than 5 (or W-5 < 0) W can't be greater than 5 (or 3W - 6 > 9)So WXYZ = 5940 is the only solution.... Show More
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H
Hermina Ferry

Feb 20, 2025

from 3) W = Z + 5, so W is at least 5. can W be more than 5? let's see what that means.if W = 6, then Y = 5, and W + Y + Z is not a single digit number. it only gets worse if W is bigger.so W must be 5, in which case, Y = 4, Z = 0 and X = 5+4+0 = 9.the number is thus5940... Show More
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H
Hermina Ferry

Feb 20, 2025

you can rewrite 2 as y=w-1this means that w+w-1+w-5=xsince they are all single digit numbers then w+w-1+w-5<=9and since z is the smallest z>=0if 3w-6=x then x must be a multiple of 3w>=5 since z>=0w<=5 since 6*3-5>9therefore w=5 now all the rest are easyw=5, x=9, y=4, z=0the integer is 5940... Show More
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