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3 years ago

Grandpa Collins is 2 years more than 25 times as his grandson Joshua. If Grandpa Collins is 77 years old, how old is Joshua?

Mathematics

1 answer:

KiRa [710]3 years ago

6 0

Answer:

3 years old is Joshua.

Step-by-step explanation:

Let y represents the age of Grandpa Collins and x represents the age of grandson Joshua.

As per the given statement: Grandpa Collins is 2 years more than 25 times as his grandson Joshua.

"25 times as his grandson Joshua" means 25x

"2 years more than 25 times as his grandson Joshua" means 25x +2

⇒ y = 25x + 2 ......[1]

Also, it is given : Grandpa Collins is 77 years old

⇒ y = 77 years

Substitute y =77 in [1] to solve for x;

77 = 25x + 2

Subtract 2 from both sides of an equation:

77 -2 =25x+2 -2

Simplify:

75 = 25x

Divide both sides by 25, we get;

$\frac{75}{25} =\frac{25x}{25}$

Simplify:

3 = x

Therefore, the age of Joshua is, 3 years old.

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2 years ago

Gabriel invested $77,000 in an account paying an interest rate of 3%

const2013 [10]

Answer:

Isabella earn $5604.54$ more money than Gabriel

Step-by-step explanation:

As we know

Compound interest (CI) $= P (1 + \frac{r}{n})^{nt}$

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t is the time period

n is the number of time periods

r is the rate of interest

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2 years ago

The following function represents the profit P(n), in dollars, that a concert promoter makes by selling tickets for n dollars ea

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A) zeroes

P(n) = -250 n^2 + 2500n - 5250

Extract common factor:

P(n)= -250 (n^2 - 10n + 21)

Factor (find two numbers that sum -10 and its product is 21)

P(n) = -250(n - 3)(n - 7)

Zeroes ==> n - 3 = 0 or n -7 = 0
Then n = 3 and n = 7 are the zeros.

They rerpesent that if the promoter sells tickets at 3 or 7 dollars the profit is zero.

B) Maximum profit

Completion of squares

n^2 - 10n + 21 = n^2 - 10n + 25 - 4 = (n^2 - 10n+ 25) - 4 = (n - 5)^2 - 4

P(n) = - 250[(n-5)^2 -4] = -250(n-5)^2 + 1000

Maximum ==> - 250 (n - 5)^2 = 0 ==> n = 5 and P(5) = 1000

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C) Axis of symmetry

Vertex = (h,k) when the equation is in the form A(n-h)^2 + k

Comparing A(n-h)^2 + k with - 250(n - 5)^2 + 1000

Vertex = (5, 1000) and the symmetry axis is n = 5.

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