Kate has three African snails named Sluggo, Pokey and SloMo. Each of these snail
ID: 3123972 • Letter: K
Question
Kate has three African snails named Sluggo, Pokey and SloMo. Each of these snails loves lettuce. One day Kate gave each snail the same number of heads of lettuce. The snails started munching away. Each snail ate at a constant rate of speed, but they were at different rates. When Sluggo had finished all of his lettuce, Pokey had 17 heads of lettuce left, and SloMo had 26 heads of lettuce left. When Pokey had finished all of his lettuce, SloMo had 12 heads left. How many heads of lettuce did each snail start with?Explanation / Answer
Let x = the number heads of lettuces given to each snail at the start
S = Rate ate which Sloggo eats the lettuces ( i.e. number of head eaten per day)
P = Rate ate which Pokey eats the lettuces
S1 = Rate ate which SloMo eats the lettuces
At the first milesston, say (T1 after day 1)
x - S(T1) = 0 <---- Equation 1
x - P(T1) = 17 <---- Equation 2
x - J(T1) = 26 <---- Equation 3
at the scond mileston (say T2)
17 - P(T2) = 0
26 - J(T2) = 12
P(T2) = 17 <---- Equation. 4
J(T2) = 14 <---- Equation. 5
divide Equation 4 by Equation 5
P/j = 17/14 <---- Equation 6
from Equation 2
P(T1) = x-17 <---- Equation 7
from Equation 3
J(T1) = x-26 <---- Equation 8
divide Equation 7 by Equation 8
P/J = (x-17)/(x-26) <---- Equation 9
from Equation 9 and Equation 6
(x-17)/(x-26) = 17/14
17(x-26) = 14(x-17)
17x - 442 = 14x - 238
17x - 14x = 442 - 238
3x = 204
x = 68 <---- answer
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.