How many eggs did the farmer have?
1 answer:
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The radical equation is 
.
i) We first isolate the square root, adding 5 to both sides of the equation:
ii) Here let's substitute x+6 with t. Doing so we have:
Squaring both sides, we get:
iii) Collecting the variables on the same side, and factorizing t we have:
, which yields
t=0 or t=1.
Now we solve for x in x+6=t:
x+6=0 ⇒x=-6 and x+6=1⇒x=-5.
iv) Now we check these values in the original equation
:
a)
⇒ 0=0 ; Correct.
b)
⇒ 1=1 ; Correct.
Answer: <span>x = −6 and x = −5 </span>
i) We first isolate the square root, adding 5 to both sides of the equation:
ii) Here let's substitute x+6 with t. Doing so we have:
Squaring both sides, we get:
iii) Collecting the variables on the same side, and factorizing t we have:
t=0 or t=1.
Now we solve for x in x+6=t:
x+6=0 ⇒x=-6 and x+6=1⇒x=-5.
iv) Now we check these values in the original equation
a)
b)
Answer: <span>x = −6 and x = −5 </span>
Answer:
a. It will take approximately 40 months
b. The total amount Paul has to pay is approximately $8,000
c. The amount Paul pays each month is approximately $316.59
d. The amount Paul has to pay is approximately $7,598.16
e. Lower monthly payment
f. Lower total payment amount (amount to be paid)
Step-by-step explanation:
a. The loan amount, PV = $7,000
The annual interest rate, r = 8%
Option 1; The amount of equal monthly payment to repay the loan = $200
Option 2; The number of equal monthly payment to repay the loan = 24
The formula for the present value of an annuity is given as follows;
Where;
PMT = The monthly payment
n = The number of months
Where PMT = $200, we have;
∴ The number of months it will take for Paul to repay the loan, n ≈ 39.988 ≈ 40 months
b. The total amount Paul has to pay, A = PMT × n
Therefore, b plugging in the values of PMT, and 'n', we get;
A ≈ $200 × 40 = $8,000
c. Using option 2, we have;
n = 24
Therefore;
The monthly payment, PMT ≈ $316.59
d. The total amount Paul has to pay using option 2, A ≈ 316.59 × 24 = 7,598.16
The total amount Paul has to pay using option 2, A ≈ $7,598.16
e. A reason why Paul might choose option 1 is that option 1 offers lower monthly payment
f. A reason why Paul may choose option 2 is that option 2 offers a lower total amount that he has to pay.