Question

Please solve this for me thank you!

Answer 1

y = $620.14 (nearest cent)

Explanation:

Given equation:

`(4y)/(1.025^4)+y-2y(1.05)^2=\$1,500`

Factor out y from the left side:

`\implies y\left((4)/(1.025^4)+1-2(1.05)^2\right)=\$1,500`

Carry out the arithmetic operations inside the parentheses by following the order of operations PEMDAS:

Calculate the exponents:

`\implies y\left((4)/(1.103812891...)+1-2(1.1025)\right)=\$1,500`

Carry out the multiplication and division from left to right:

`\implies y\left(3.623802579...+1-2.205\right)=\$1,500`

Carry out the addition and subtraction from left to right:

`\implies y\left(4.623802579...-2.205\right)=\$1,500`

`\implies y\left(2.418802579...\right)=\$1,500`

Finally, divide both sides by the coefficient of y to isolate y:

`\implies (y\left(2.418802579...\right))/(2.418802579...)=(\$1,500)/(2.418802579...)`

`\implies y=\$620.141558...`

Therefore, y = $620.14 (nearest cent)

Answer 2

620.14

Explanation:

Original Equation:

`(4y)/(1.025^4)+y-2y(1.05)^2=1500`

Calculate exponents

`(4y)/(1.103812890625)+y-2y(1.1025)=1500\\`

Simplify:

`3.6238025791990193084270042653997y + y - 2.205y = 1500`

Add like terms

`2.4188025791990193084270042653997y \approx 1500`

Divide both sides by 7.012

`y\approx 213.91`
`y\approx620.14`