Question

Pls help explain your thinking

Answer 1

Mouse = 7

Hedgehog = 6

Owl = 4

Final equation = -2

Explanation:

Define the variables:

• Let x = mouse.
• Let y = hedgehog.
• Let z = owl.

The variables in the second equation are the same. Therefore, begin with this equation to determine the value that the mouse represents (x):

`\begin{aligned} \implies\sf Mouse + Mouse * Mouse + Mouse &=63\\ x+x * x+x&=63\end{aligned}`

Following the order of operations, carry out the multiplication first:

`\implies x+x^2+x=63`

Add the like variables:

`\implies x^2+2x=63`

Subtract 63 from both sides:

`\implies x^2+2x-63=0`

Factor and solve for x:

`\implies x^2+9x-7x-63=0`

`\implies x(x+9)-7(x+9)=0`

`\implies (x-7)(x+9)=0`

`\implies x-7=0 \implies x=7`

`\implies x+9=0 \implies x=-9`

Therefore, the two possible values of the x are 7 and -9.

Evaluate the third equation where there are two variables:

`\begin{aligned} \implies\sf Hedgehog * Hedgehog - Hedgehog + Mouse &=37\\ y * y-y+x&=37\end{aligned}`

Carry out the multiplication first:

`\implies y^2-y+x=37`

Subtract 37 from both sides:

`\implies y^2-y+x-37=0`

As we have two possible values for x, substitute each value into the equation and solve for y.

Substitute x = 7 and solve for y:

`\implies y^2-y+7-37=0`

`\implies y^2-y-30=0`

`\implies y^2-6y+5y-30=0`

`\implies y(y-6)+5(y-6)=0`

`\implies (y+5)(y-6)=0`

`\implies y+5=0 \implies y=-5`

`\implies y-6=0 \implies y=6`

Substitute x = -9 and solve for y:

`\implies y^2-y-9-37=0`

`\implies y^2-y-46=0`

Using a calculator:

`\implies y=(1 \pm √(185))/(2)`

Assuming the numbers should be integers, we can discount x=-9 as it gives a non-integer value of y.

Therefore:

• x = 7
• y = -5 or y = 6

Evaluate the first equation where there are two variables:

`\begin{aligned} \implies\sf (Hedgehog + Owl) * (Hedgehog - Owl)&=20\\ (y+z) *(y-z)&=20\end{aligned}`

Simplify this equation and isolate z²:

`\implies (y+z) * (y-z)=20`

`\implies y^2-zy+zy-z^2=20`

`\implies y^2-z^2=20`

`\implies z^2=y^2-20`

As we have two possible values for y, substitute each value and solve for z.

Substitute y = -5 and solve for z:

`\implies z^2=(-5)^2-20`

`\implies z^2=25-20`

`\implies z^2=5`

`\implies z=√(5)`

Substitute y = 6 and solve for z:

`\implies z^2=6^2-20`

`\implies z^2=36-20`

`\implies z^2=16`

`\implies z=4`

Again, assuming the numbers should be integers, we can discount y=-5 as it gives a non-integer value of z. Therefore:

• y = 6
• z = 4

Therefore, we have determined that:

• Mouse (x) = 7
• Hedgehog (y) = 6
• Owl (z) = 4

Substitute the found values into the fourth equation and solve:

`\begin{aligned}\implies \sf Owl + Mouse - Hedgehog - Mouse &=z+x-y-x\\&=4+7-6-7\\&=11-6-7\\&=5-7\\&=-2\end{aligned}`