Luis spent a certain amount of money in a supermarket. He spent a thir

Official Solution:

Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, \($12\) on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?

A. \(60\)
B. \(66\)
C. \(72\)
D. \(78\)
E. \(84\)


Let the amount Luis spent in the supermarket be \($x\).

Luis spent a third of the money on fruits \(=\frac{x}{3}\);

Luis spent a sixth of the money on vegetables \(=\frac{x}{6}\);

Luis spent \($12\) of the money on pasta \(=12\);

Luis spent half the remainder of the money on chocolate \(=(x-(\frac{x}{3}+\frac{x}{6}+12))*\frac{1}{2}=\frac{x}{4}-6\);

Luis spent s much on soda as he spent on vegetables \(=\frac{x}{6}\).

So, we have that \(\frac{x}{3}+\frac{x}{6}+12+(\frac{x}{4}-6)+\frac{x}{6}=x\);

\(x=72\).


Answer: C

Say the total money be x.

The Eqn:

\(\frac{x}{3}\) + \(\frac{x}{6}\) + \(12\) + \(\frac{1}{2}\) ( \(x\) - \(\frac{x}{3}\) - \(\frac{x}{6}\) - \(12\) ) + \(\frac{x}{6}\) = \(x\)

Now solving for \(x\) , we get the total money as \(72\) ..... Ans C.

Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, $12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?

A. 60
B. 66
C. 72
D. 78
E. 84

Given : Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, $12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables.

Asked: How much money did Luis spend in the supermarket?

Let the money he spend in the supermarket be x

Money spent on fruits = x/3
Money spent on vegetables = x/6
Money spent on fruits and vegetables = x/3+x/6 =x/2
Money spent on pasta = $12
Remaining money = x - (x/2 + 12) = x/2 -12
Money spent on chocolate = x/4 - 6
Money spent on soda = x/6

Total money spent = x/2 + 12 + x/4 -6 + x/6 = x
11x/12 +6 = x
x/12 = 6
x = 12*6 = 72

IMO C

Let the amount is x, then as per question:
Fruits: \(\frac{x}{3}\)
Vegetables: \(\frac{x}{6}\)
Pasta: 12
Remainder x - (\(\frac{x}{3}\) + \(\frac{x}{6}\) +12) = \(\frac{x-24}{2}\)
but chocolate was at half of the remainder:
\(\frac{x-24}{4}\)
And, Soda = \(\frac{x}{6}\)

Thus:
\(\frac{x}{3}\) + \(\frac{x}{6}\) + 12 + \(\frac{x-24}{2}\) + \(\frac{x}{6}\) = x

Solving this:
11x + 72 = 12x
x = 72

IMO the answer is C.

Please hit kudos if you like the solution.

Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, $12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?

A. 60
B. 66
C. 72
D. 78
E. 84

(a third of the money on fruits) + ( a sixth on vegetables) = 1/3 + 1/6 = 1/2 = 50 %

thus after this , only 50% or 1/2 were spent

Now, (on soda) = (on vegetables) =1/6

but since on chocolate it is mentioned as half of the remainder after pasta, so.... (on soda) = (on chocolates) = 1/6

=> (on soda) + (on chocolates) = 1/3.


Now,

1 - (a third of the money on fruits) + ( a sixth on vegetables) + (on soda) + (on chocolates) = $12

=> 1 - 1/2 + 1/3 = $12 =1/6
=> total spent = 12*6 = $72

Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, $12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?

A. 60
1/3 of $60 for fruits = $20
1/6 of $60 for vegetables = $10
$12 on pasta
$60-$20-$10-$12=$18-remainder
half of reminder for chocolate = $9
and as much on soda as he spent on vegetables, but $9 not equal to $10
incorrect

B. 66
1/3 of $66 for fruits = $22
1/6 of $66 for vegetables = $11
$12 on pasta
$66-$22-$11-$12=$21-remainder
half of reminder for chocolate = $10.5
and as much on soda as he spent on vegetables, but $10.5 not equal to $11
incorrect

C. 72
1/3 of $72 for fruits = $24
1/6 of $72 for vegetables = $12
$12 on pasta
$72-$24-$12-$12=$24-remainder
half of reminder for chocolate = $12
and as much on soda as he spent on vegetables, $12 equal to $12
Bingo

D. 78
1/3 of $78 for fruits = $26
1/6 of $78 for vegetables = $13
$12 on pasta
$78-$26-$13-$12=$27-remainder
half of reminder for chocolate = $13.5
and as much on soda as he spent on vegetables, but $13.5 not equal to $13
incorrect

E. 84
1/3 of $84 for fruits = $28
1/6 of $84 for vegetables = $14
$12 on pasta
$84-$28-$14-$12=$30-remainder
half of reminder for chocolate = $15
and as much on soda as he spent on vegetables, but $15 not equal to $14
incorrect

C is the answer.

Alegbra PS

Posted from my mobile device

Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, $12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?

Solution:
Let say total money, Luis spend in the supermarket=t
a third of the money on fruits = t/3
a sixth on vegetables=t/6
on pasta = $12 &
half the remainder of the money on chocolate = (t-t/3-t/6-12)/2
as much on soda as he spent on vegetables = t/6 = remaining half of the money = (t-t/3-t/6-12)/2
=> t/3 = t - t/3 - t/6-12
=> t-t/3-t/3-t/6 = 12
=> (6t-2t-2t-t)/6=12
=>t/6=12
=> t=72


A. 60
B. 66
C. 72 --> correct
D. 78
E. 84

Let the total amount be x
hence equation is

\(\frac{x}{3}+ \frac{x}{6} + 12 + \frac{x}{4} -6 = x\)
solve for x
after solving the equation x= 72
which is C