suppose five bales of hay are weighed two at a time in all the possible ways. the wieghts in pounds are 110, 112, 113, 114, 115, 116, 117,118,120,121 how much does each bale of hay weigh?
2006-08-28 11:35:26 · 2 answers · asked by rushin_13 2 in Science & Mathematics ➔ Mathematics
dimos answer is off a little bit
first assign the five bales of hay as variables a-e, with a weighing the least and e weighing the most
a + b = 110
a + c = 112
a + d = 113
a + e = 114
b + c = 115
b + d = 116
b + e = 117
c + d = 118
c + e = 120
d + e = 121
by adding these equations we have
4(a + b + c + d + e) = 1176
a + b + c + d + e = 289
c = 289 - (a + b) - (d + e) (you must solve for c first)
c = 289 - 110 - 121
c = 68
once you know that c = 58, then
a = 112 - 58 = 54
b = 110 - 54 = 56
d = 121 - 63 = 58
e = 121 - 58 = 63
a = 54
b = 56
c = 58
d = 58
e = 63
2006-08-28 13:26:50 · answer #1 · answered by Anonymous · 1⤊ 0⤋
If a, b, c, d, e are the weights then we have:
a + b = 110
a + c = 112
a + d = 113
a + e = 114
b + c = 115
b + d = 116
b + e = 117
c + d = 118
c + e = 120
d + e = 121
by adding these equations we have:
4(a + b + c + d + e) = 1156
a + b + c + d + e = 289
e = 289 - (a + b) - (c + d)
e = 289 - 110 - 118
e = 61
By substitution we get:
a = 54, b = 56, c = 59, d = 60 and e = 61
2006-08-28 12:19:29 · answer #2 · answered by Dimos F 4 · 0⤊ 0⤋