one number is three more than a second number. Three times the first is 7 less than 2 times the second. Find the numbers.
The value of the second number is ___
second number ---- x
first number ------ x+3
A lot of students have difficulty translating an English inequality statement like "Three times the first is 7 less than 2 times the second" into an equation.
Here is the way I used to teach this: ..
Re-word the statement as
"Three times the first is less than 2 times the second by 7"
now translate that
3(x+3) < 2(x) by 7
let's add that difference of 7 to the smaller side, now they would be equal
3(x+3) + 7 = 2(x)
3x + 9 + 7 = 2x
x = -16
so second number is -16, he first is -13
check:
3 times the first = 3(-13) = -39
2 times the second = 2(-16) = -32
is -39 7 less than -32 ??? YEAHH!
To solve this problem, let's assume the first number as 'x' and the second number as 'y'.
The first statement tells us that "one number is three more than a second number." So we can write the equation as:
x = y + 3
The second statement tells us that "three times the first is 7 less than 2 times the second." So we can write the equation as:
3x = 2y - 7
Now, we can solve this system of equations to find the values of 'x' and 'y'.
1) Substitute the value of x from the first equation into the second equation:
3(y + 3) = 2y - 7
2) Simplify and solve for y:
3y + 9 = 2y - 7
3y - 2y = -7 - 9
y = -16
So, the value of the second number (y) is -16.