Question

His question has three parts. Answer the parts in order.

Part 1

Brit is 10 years older than her brother Tyrese. She is also 3 times as old as Tyrese.

Select two equations of a system that can be solved to find both ages.
A. y = 10 - x
B. y = 3x
C. x = 3y
D. x - y = 10

Part 2

How many years old is Brit? (Use only the digits 0 – 9 to enter a number.)

Part 3

How many years old is Tyrese? (Use only the digits 0 – 9 to enter a number.)

Answer 1

1) C. x = 3y

D. x - y = 10

2) Brit is 15 years old.

3) Tyrese is 5 years old.

Explanation:

Part 1

Given information:

• Brit is 10 years older than her brother Tyrese.
• Brit is 3 times as old as Tyrese.

Let "x" be Brit's age (in years).

Let "y" be Tyrese's age (in years).

If Brit is 10 years older than her brother Tyrese, then if we subtract Tyrese's age from Brit's age, we get 10. Therefore, the equation that models this is:

`\large\boxed{x-y=10}`

If Brit is 3 times as old as Tyrese, then the equation that models this is:

`\large\boxed{x=3y}`

`\hrulefill`

Part 2

We now have a system of linear equations:

`\begin{cases}x-y=10\\x=3y\end{cases}`

To solve the equation for x (Brit's age), rewrite the first equation to isolate y:

`\begin{aligned}x-y&=10\\x-y+y&=10+y\\x&=10+y\\x-10&=10+y-10\\x-10&=y\\y&=x-10\end{aligned}`

Substitute the found expression for y into the second equation, then solve for x:

`\begin{aligned}x&=3y\\x&=3(x-10)\\x&=3x-30\\x+30&=3x-30+30\\x+30&=3x\\x+30-x&=3x-x\\30&=2x\\30/2&=2x/2\\15&=x\\x&=15\end{aligned}`

Therefore, Brit is 15 years old.

`\hrulefill`

Part 2

To find Tyrese's age, substitute the found value of x into the rearranged first equation and solve for y:

`\begin{aligned}y&=x-10\\y&=15-10\\y&=5\end{aligned}`

Therefore, Tyrese is 5 years old.

Answer 2

Part A:

• C. x = 3y
• D. x - y = 10

Part B: Brit is 15 years old.

Part C: Tyrese is 5 years old.

Explanation:

Part 1

Let age of brit be x and her brother be y.

Brit is 10 years older than her brother Tyrese.

It can be said mathematically as:

x = 10+y

x-y=10

She is also 3 times as old as Tyrese.

x = 3y

Therefore, The correct answers for Part 1 are C and D.

Part 2 and Part 3

We can find the value of x by substituting x = 3y in equation x-y = 10.

We get:

3y-y = 10

2y = 10

`\sf y = (10)/(2)`

y = 5

Therefore, Tyrese is 5 years old.

Again,

substituting value of y in equation x-y = 10.

We get:

x - 5 =10

x = 10+5

x = 15

Therefore, Brit is 15 years old.