help...again?

Question

you teacher is giving a test worth 150 pts. there are 46 three and 5 point questions . how many of each are on the test?

Answer 1

x = number of three point questions
y = number of five point questions

x + y = 46
3x + 5y = 150

In the first equation, y = 46 - x. This can be substituted into the second equation.

3x + 5(46 - x) = 150
3x + 230 - 5x = 150
-2x = -80
x = 40

x + y = 46
40 + y = 46
y = 6

There are 40 3-point questions and 6 5-point questions.

Answer 2

Let x = three poing questions
and
Let y = 5 poing questions

The first equation would be:

x + y = 46

(i got this because the total of three point questions and 5 poing questions equal to 46)

the second would be:

3x + 5y = 150

(i got this because the total points of the test are 150)

Multiplying the first equation by -3 gives us:

-3x + -3y = -138

Combining this with the second equation gives us:

2y = 12

which implies that y = 6 !
we're halfway there!

plugging in 6 for y in the first equation gives us:

x + 6 = 46

or x = 40!

so the final answer would be that there are 40 3point questions and 6 5point questions on the test.


please choose this as best answer.
and if you need more help with math, feel free to email me

Answer 3

a: number of questions worth five points
b: number of questions worth three points

We know:

a + b = 46
5a + 3b = 150

b = 46 - a [from first equation]

5a + 3b = 150
5a + 3(46 - a) = 150
5a + 138 - 3a = 150
2a + 138 = 150
2a = 150 - 138
2a = 12
a = 6
b = 46 - a = 40

There are forty three-points questions, and five five-points questions

Answer 4

x+y=46
3x+5y=150


y=6
x=40