Photos

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

Final 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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