Photos

Three friends, Mirka, Lucka, and Hanka, collect photos. If Mirka had three more photos, she would have as many as Hanka. If Lucka had five photos less than she has, she would be like Hanka. How many photographs does each have if they have 431 together?

Correct answer:

H =  143
L =  148
M =  140

Step-by-step explanation:


M+L+H = 431
M+3 = H
L-5 = H

H+L+M = 431
H-M = 3
H-L = -5

Row 2 - Row 1 → Row 2
H+L+M = 431
-L-2M = -428
H-L = -5

Row 3 - Row 1 → Row 3
H+L+M = 431
-L-2M = -428
-2L-M = -436

Pivot: Row 2 ↔ Row 3
H+L+M = 431
-2L-M = -436
-L-2M = -428

Row 3 - -1/-2 · Row 2 → Row 3
H+L+M = 431
-2L-M = -436
-1.5M = -210


M = -210/-1.5 = 140
L = -436+M/-2 = -436+140/-2 = 148
H = 431-L-M = 431-148-140 = 143

H = 143
L = 148
M = 140

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