Solve the problem.
-The sale price on an outfit Sally wanted was a 5-digit palindromic number, say $abc.de, satisfying the given conditions:
Sally would never pay over $\$ 200.00$;
b, c, and d are all multiples of 3 ;
$c = ( d + b ) - 12 ;$
the sum of all the digits is a multiple of 13;
$\mathrm { a } + \mathrm { e } = ( \mathrm { b } + \mathrm { d } ) - 16 ; \text { and } \mathrm { c } = 3 ( \mathrm { a } + \mathrm { e } ) \text {. }$
What amount does she owe the salesperson?
A) $\$ 296.92$
B) $\$ 196.91$
C) $\$ 136.31$
D) $\$ 193.91$

Question

Solve the problem.
-The sale price on an outfit Sally wanted was a 5-digit palindromic number, say $abc.de, satisfying the given conditions: 
Sally would never pay over $\$ 200.00$;
b, c, and d are all multiples of 3 ;
$c = ( d + b ) - 12 ;$
the sum of all the digits is a multiple of 13;
$\mathrm { a } + \mathrm { e } = ( \mathrm { b } + \mathrm { d } ) - 16 ; \text { and } \mathrm { c } = 3 ( \mathrm { a } + \mathrm { e } ) \text {. }$
What amount does she owe the salesperson?
A) $\$ 296.92$
B) $\$ 196.91$
C) $\$ 136.31$
D) $\$ 193.91$

Quizplus · Accepted Answer

Given the constraints, we can deduce the following:- The price is a 5-digit palindromic number under $200.00, meaning $a = 1$ and $e = 1$.- $b$, $c$, and $d$ are multiples of 3.- $c = (d + b) - 12$.- The sum of all digits is a multiple of 13.- $a + e = (b + d) - 16$; since $a = 1$ and $e = 1$, $2 = (b + d) - 16$, so $b + d = 18$.- $c = 3(a + e) = 3(2) = 6$.Given $b + d = 18$ and both are multiples of 3, and $c = 6$, the closest values that satisfy these conditions are $b = 9$ and $d = 9$. This makes the price $196.91, which is under $200.00, and the sum of the digits $1 + 9 + 6 + 9 + 1 = 26$, which is a multiple of 13.

Solve the Problem $200.00\$ 200.00$200.00 ; B, C, and D Are All Multiples of 3

Solve the Problem $\$ 200.00$ ;
B, C, and D Are All Multiples of 3