Question 155748
1) find 4 consecutive even integers such that the sum of twice the first, five times the second and four times the third divided by three times the fourth equals 3.
:
4 consecutive integers: x, x+2, x+4, x+6
:
Write an equation for the statement:
"the sum of twice the first, five times the second and four times the third divided by three times the fourth equals 3."
{{{((2x + 5(x+2) + 4(x+4)))/(3(x+6))}}} = 3
:
{{{((2x + 5x + 10 + 4x + 16))/(3x+18))}}} = 3
:
{{{((11x + 26))/(3x+18))}}} = 3
Multiply both sides by (3x+18)
11x + 26 = 3(3x + 18)
:
11x + 26 = 9x + 54
:
11x - 9x = 54 - 26
:
2x = 28
x = {{{28/2}}}
x = 14
:
The four numbers: 14, 16, 18, 20
:
Check the solutions in the statement:
"the sum of twice the first, five times the second and four times the third divided by three times the fourth equals 3."
{{{((2(14) + 5(16) + 4(18)))/(3(20))}}} = 3
{{{((28 + 80 + 72))/(60)}}} = 3
{{{180/60}}} = 3
:
:
2) Find three consecutive odd integers such that 4 less than twice the second has the same value as three times the number that is one more that the third.
:
We have: x, (x+2), (x+4) as the three consecutive odd numbers
:
2(x+2)- 4 = 3(x+4+1)
2x + 4 - 4 = 3(x+5)
2x = 3x + 15
2x = 3x = 15
-x = 15
x = -15
;
The numbers: -15, -13, -11
:
;
Check:
2(-13) - 4 = 3(-11+1)
-26 - 4 = 3(-10)