Respuesta :
Answer:
Arica gave to each charity $14, $7 and $ 56 respectively.
Step-by-step explanation:
Arica planned to donate a total $89 to four charities.
She donated twice as much to Charity A as she did to charity B.
Let she donated $x to charity A.
So, she donated $[tex]\frac12x[/tex] to charity B
But she donated only [tex]\frac14[/tex] as much to charity A as to charity C.
So, she donated $4x to charity C.
She gave $12 to charity D.
So she total donated [tex]=\$(x+\frac12x+4x+12)[/tex]
According to the problem,
[tex]x+\frac12x+4x+12=89[/tex]
[tex]\Rightarrow \frac{2x+x+8x}4+12=89[/tex]
[tex]\Rightarrow \frac{11x}2=89-12[/tex]
[tex]\Rightarrow \frac{11x}2=77[/tex]
[tex]\Rightarrow x=\frac{77\times2}{11}[/tex]
⇒x=14
The amount that she gave to charity A is $14
The amount that she gave to charity B is= [tex]\frac12x[/tex]
[tex]=\$\frac12 \times 14[/tex]
=$7
The amount that she gave to charity C is= 4x
=$(4×14)
=$56
Arica must give $14, $7, $56, and $12 to Charity A, B, C, and D.
What is the amount donated to each charity?
As it is given to us that Arica wanted to give twice as much to Charity A as she did to Charity B, but only one-fourth as much to Charity A as to Charity C. therefore,
A = 2B
C = 4A
where A, B, C, and D denote the amount given to charity A, B, C, and D respectively.
We know that the total amount with Arica is $89. therefore,
A + B + C + D = $89
we know that A = 2B and C = 4A, substitute the values,
A + B + C + D = $89
(2B) + B + C + D = $89
(2B) + B + (4A) + D = $89
(2B) + B + 4(2B) + D = $89
2B + B + 8B + D = $89
11 B + D = $89
11B + $12 = $89
11 B = 77
B = $7
Substitute the values,
B= $7
A = 2B = $14
C = 4A = 4(14) = $56
Hence, Arica must give $14, $7, $56, and $12 to Charity A, B, C, and D.
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