Egor was to be paid 100 groats plus a shiny new belt buckle if he worked for Lord Xerxes for one year. However, Egor had to leave after working for only seven months. Lord Xerxes gave Egor fair payment of 20 groats plus the shiny new belt buckle for his work. How many groats is the belt bucke worth?
2007-03-22 02:17:28 · 7 answers · asked by babigurl34 2 in Science & Mathematics ➔ Mathematics
set up equation (100+x)/ 12 = (20+x)/7
cross multiply --> 700 +7x = 240 + 12x
Solve for x --> 460 = 5x --> x= 92 groats
2007-03-22 02:23:34 · answer #1 · answered by Doctor B 2 · 1⤊ 0⤋
Hi1 The outstanding 5 months are worth 80 groats, divide this by 5 to get 16 groats.
Egor worked 7 months (7 * 16 =112) and was paid 20 groats. Deduct the 20 groats from this giving a balance of 92 groats. to check this multiply 16 by 12 to give 192 (Egors 100 plus the belt) Hope this helps.
2007-03-22 09:34:21 · answer #2 · answered by ray trigg 1 · 0⤊ 0⤋
If Egor worked for only 7 months out of 12 (one year), he received 7/12 of the promised fee, which was 100 groats and the belt buckle worth the unknown amount x groats. That means that his annual salary was to be 100 + x, and he was actually paid 20 + x. The algebra proceeds as follows.
(7/12)(100 + x) = 20 + x
700/12 + 7x/12 = 20 + x
(700 - 240)/12 = (12 - 7)x/12
460 = 5x
x = 92 groats
Note that I rewrote 20 as 240/12 and x as 12x/12 so that I could more easily combine terms.
2007-03-22 09:24:24 · answer #3 · answered by DavidK93 7 · 1⤊ 0⤋
Let x be the value of the belt buckle.
The total value of a year's work is 100 + x
The total value of 7/12 year's work is 20 + x
Hence, your equation is:
20 + x = 7/12 * (100 + x)
Multiplying by 12 to clear out the fractions:
12 * (20 + x) = 7 * (100 + x)
240 + 12x = 700 + 7x
5x = 460
x = 92
The belt buckle is worth 92 groats.
2007-03-22 09:23:45 · answer #4 · answered by Bramblyspam 7 · 1⤊ 0⤋
Ans:
Let the value of the belt buckle be x
One year work is=100 + x
And total value of 7/12 year's work =20 + x
Therefore,
20 + x = 7/12 * (100 + x)
12(20+x)=7(100+x)
240+12x=700+7x
12x-7x=700-240
5x=460
x=460/5
=92
Good Luck
2007-03-22 09:40:12 · answer #5 · answered by ckoottunkal 2 · 0⤊ 0⤋
100 goats + 1 buckle = 12 months ---1
20 goats + 1 buckle = 7 months ---2
take the first statement minus 2nd statement: you will get
50 goats= 5 months
in other words, 100 goats= 5 x 2 months
100 goats =10 months
and so in accordance to statement 1,
12 months =120 goats
therefore statement 1 becomes
100 goats + 1 buckle = 120 goats
thus 1 buckle= 20 goats
2007-03-22 09:30:29 · answer #6 · answered by llcold 2 · 0⤊ 1⤋
38 goats ( if point 1 doesn't matter)
2007-03-22 09:22:15 · answer #7 · answered by MDA 4 · 0⤊ 3⤋