Question

My friend Tott bought 7 hopts and 3 alabers for a total cost of $85. My

friend Froph bought 1 hopts and 4 alabers for a total cost of $30.
Here are equations showing the relationship between cost of hopts (x)
and cost of alabers (y):
x + 4y = 30
7x+3y=85
What were the prices for hopts and alabers?

Answer 1

Hopt is $10

Alaber is $5

Explanation:

we are given the system of equations:

`x + 4y = 30 \\ 7x + 3y = 85`

we can start by multiplying the first equation by 7.

`7x + 28y = 210`

next, subtract the equations. we will get

`28y - 3y = 21 0 - 85`

this simplifies to

`25y = 125`

and dividing both sides by 25 we get y = 5.

substitute back to the original equation:

`x + 4(5) = 30`

subtract 20 from both sides and you'll get x = 10.

so, the solution is (x, y) = (10, 5)