Problema Solution
the relation between the cost of a certain gem and its weight is linear. In looking at two gems, we find that one of the gems weighs 0.3 carat and cost $3542, while the other gem weighs 0.6 carat and cost $4380. Find the linear function
Answer provided by our tutors
let
y = the cost of the gem
x = the weight of the gem
the relation between the cost of a certain gem and its weight is linear means:
y = ax + b, where a and b are constants
we need to find a and b
we find that one of the gems weighs 0.3 carat and cost $3542:
y = $3542, x = 0.3 carats
3542 = 0.3a + b
while the other gem weighs 0.6 carat and cost $4380:
y = $4380, x = 0.6 carats
4380 = 0.6a + b
by solving the system of equations:
0.3a + b = 3542
0.6a + b = 4380
we find:
a = 8380/3
b = 2704
click here to see the step by step solution of the system of equations:
the linear function is:
y = (8380/3)x + 2704