Use either the substitution or elimination method to solve the following word problem. Your answer should include two equations and the solution to the two equations: Ed and his little sister are saving up money to buy a joint birthday present for their mother. Ed already owes a friend $1, and plans to save $6 per week from his allowance. His sister has $2.66 saved so far and will also save $6 per week from her allowance. The two siblings will soon have saved the same amount towards their mother's gift. How much will each one have saved? How long will that take?

Step-by-step explanation:

Represent Ed's savings with e and his sister's by s.

Then the function representing Ed's savings is

e(t) = -$1 + ($6/wk)t, where -$1 is the amount he owes and ($6/wk)t represents the amount he will receive from savings.

The function representing his sister's savings is

s(t) = $2.66 + ($6/wk)t

If we equate these two equations and solve the resulting system for e and s, we'll get:

e(t) = -$1 + ($6/wk)t = s(t) = $2.66 + ($6/wk)t

Then $2.66 + ($6/wk)t  =   -$1 + ($6/wk)t

Combining like terms results in:

$3.66 = ($6/wk)t, which we solve for t:

      $3.66

t = = 0.61 week, which is equivalent to approx. 4 1/2 days.

      ($6/wk)t

The siblings will have the same amount saved after 4 1/2 days, and that amount will be approximately  $2.66 + ($6/wk)(0.61 wk) = $6.32

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

the answer to this question is 3/19

step-by-step explanation: