Let A be Angel's money, B be Braulio's money and K be Keoni's money. Now translate English to algebra:
B = 3A - 1 .... "one less than triple Angel's money"
K = B + 6 .... "six more than Braulio's money"
Use the first equation to substitute for B in the second:
K = (3A - 1) + 6
K = 3A + 5 .... and simplify by combining like terms
Finally, you were told:
A + B + K = 60 .... "their money totals $60"
A + (3A - 1) + (3A + 5) = 60 .... use the above results to substitute for B and K
7A + 4 = 60 .... combine like terms and solve the two-step equation
7A = 56
A = 8
Now you know Angel had $8. Use that fact and the above results to find B and K:
B = 3A - 1 = (3)(8) - 1 = 24 - 1 = 23 .... Braulio had $23
K = 3A + 5 = (3)(8) + 5 = 24 + 5 = 29 .... Keoni had $29
Check: 23 is indeed 1 less that three times 8, and 29 is indeed 6 more than 23. Good so far. Finally 8 + 23 + 29 = 8 + 52 = 60 shows that the solution satisfies all given facts.
4x - 4 = 180 ------> this is incorrectly shown as 4x - 1 = 180
Divide both sides by 4
(4x - 4)/4 = 180/4 -----> this is incorrectly shown as 4x/4 - 1
since you should divide all terms by 4
However because of error in previous step
final result will be correct
x - 1 = 45
x = 45 + 1
x = 46
NOTE: even though the work shown arrives at correct answer, you will never get full marks. Two errors that cancel out to give correct result will cost you points.
Answers & Comments
Verified answer
14 12/9 = 60/(x - 1)
12(x - 1) = 9 x 60.............cross multiply
(x - 1) = 9 x 5 .........dividing through by 12
x - 1 = 45
x = 46
17 h/16 = 4/10
h = 16 x 2/5
= 32/5
= 6.4
19 Let x = Angel's money
3x - 1 = Braulio's money
3x - 1 + 6 = Keoni's money
x + 3x - 1 + 3x - 1 + 6 = 60
7x + 4 = 60
7x = 56
x = 8
Angel = $8
Braulio = $23
Keoni = $29
Let A be Angel's money, B be Braulio's money and K be Keoni's money. Now translate English to algebra:
B = 3A - 1 .... "one less than triple Angel's money"
K = B + 6 .... "six more than Braulio's money"
Use the first equation to substitute for B in the second:
K = (3A - 1) + 6
K = 3A + 5 .... and simplify by combining like terms
Finally, you were told:
A + B + K = 60 .... "their money totals $60"
A + (3A - 1) + (3A + 5) = 60 .... use the above results to substitute for B and K
7A + 4 = 60 .... combine like terms and solve the two-step equation
7A = 56
A = 8
Now you know Angel had $8. Use that fact and the above results to find B and K:
B = 3A - 1 = (3)(8) - 1 = 24 - 1 = 23 .... Braulio had $23
K = 3A + 5 = (3)(8) + 5 = 24 + 5 = 29 .... Keoni had $29
Check: 23 is indeed 1 less that three times 8, and 29 is indeed 6 more than 23. Good so far. Finally 8 + 23 + 29 = 8 + 52 = 60 shows that the solution satisfies all given facts.
14. Multiply by 9(x -1)
.. 12(x -1) = 60*9
.. x -1 = 45 . . . divide by 12
.. x = 46 . . . add 1
17. It usually works well to make sure the variable of interest is at the top of one of the ratios.
.. h/4 = 16/10
.. h = 4*16/10 = 6.4
19. Let a, b, k represent the money in dollars held by Angel, Braulio, and Keoni, respectively. We are asked to find the value of k.
.. b = 3a -1
.. k = b +6
.. a +b +k = 60 . . . their money totals $60
We can solve the second equation for b.
.. b = k -6
Then we can substitute into the first equation and solve for a.
.. k -6 = 3a -1
.. k -5 = 3a . . . add 1
.. (k -5)/3 = a . . . divide by 3
Now, we can write the total amount in terms of k
.. (k -5)/3 + (k -6) + k = 60
.. k -5 +3(k -6) +3k = 180 . . . multiply by 3
.. 7k -23 = 180 . . . collect terms
.. 7k = 203 . . . add 23
.. k = 203/7 = 29
Keoni has $29.
12/9 = 60/(x-1)
Simplifying left side we get:
4/3 = 60(x-1)
Cross multiplying we get:
4(x-1) = 3*60
4x - 4 = 180 ------> this is incorrectly shown as 4x - 1 = 180
Divide both sides by 4
(4x - 4)/4 = 180/4 -----> this is incorrectly shown as 4x/4 - 1
since you should divide all terms by 4
However because of error in previous step
final result will be correct
x - 1 = 45
x = 45 + 1
x = 46
NOTE: even though the work shown arrives at correct answer, you will never get full marks. Two errors that cancel out to give correct result will cost you points.