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Question

Kira, Alan, and Henry sent a total of 122 text messages over their cell phones during the weekend. Kira sent 8 fewer messages than Alan. Henry sent 4 times as many messages as Kira. How many messages did they each send?

Answer 1

K-Kira, A-Alan, H-Henry

K + A + H = 122

K = A - 8 --> A = K + 8

H = 4K

K + A + H = 122

K + (K + 8) + (4K) = 122

6K + 8 = 122

6K = 114

K = 19

A = K + 8 = 19 + 8 = 27

H = 4K = 4*19 = 76

Kira sent 19, Alan 27 and Henry 76

Answer 2

K + A + H = 122

K = A - 8. Rearrange, A = K + 8

H = 4K

Substitute Eq 2 and 3 into Eq 1

K + K + 8 + 4K = 122

6K = 114

K = 114 / 6 = 19

A = K + 8 = 19 + 8 = 27

H = 4K = 4 x 19 = 76