Question

Can you help me please?The sum of two numbers is 46. The sum of 6 times the larger and 4 times the smaller is 238. What’s the larger number and the smaller number

Answer 1

We have:

The sum of two numbers is 46: x + y = 46

The sum of 6 times the larger and 4 times the smaller is 238: 6x + 4y = 238

Where

x = the larger number

y = the smaller number

Solve the system of equations:

`\begin{gathered} x+y=46 \\ 6x+4y=238 \end{gathered}`

So:

`\begin{gathered} x+y-x=46-x \\ y=46-x \end{gathered}`

Substitute y in the second equation:

`6x+4(46-x)=238`

Simplify and solve for x:

`\begin{gathered} 6x+184-4x=238 \\ 2x+184=238 \\ 2x+184-184=238-184 \\ 2x=54 \\ (2x)/(2)=(54)/(2) \\ x=27 \end{gathered}`

Then for y:

`y=46-27=19`

Answer:

larger number: 27

smaller number: 19