Respuesta :
Answer:
Daniel had total $70 before shopping.
Step-by-step explanation:
Let us assume that Daniel had total money before shopping = $x.
He spent [tex]\frac{2}{5}[/tex] of total money on books, that is = $[tex]\frac{2}{5}[/tex] of x= [tex]\frac{2}{5}[/tex] x.
Remaining money with him = (x-[tex]\frac{2}{5}[/tex] x) .
And spent 1/3 of the remaining that is 1/3 of (x-2/5x) = 1/3(x-[tex]\frac{2}{5}[/tex] x) on food.
Money left with him = $28.
Therefore, we can setup and equation.
Money spent on books + Money spent on food + Remaining money = Total money before shopping.
Substituting above values in equation, we get
[tex]\frac{2}{5}[/tex] x + [tex]\frac{1}{3}[/tex](x-[tex]\frac{2}{5}[/tex] x) + 28 = x.
Subtracting x-[tex]\frac{2}{5}[/tex] x = [tex]\frac{5x}{5}[/tex] - [tex]\frac{2x}{5}[/tex] = [tex]\frac{3x}{5}[/tex], we get
[tex]\frac{2}{5}[/tex] x + [tex]\frac{1}{3}[/tex]([tex]\frac{3x}{5}[/tex]) + 28 = x.
Multiplying [tex]\frac{1}{3}[/tex]([tex]\frac{3x}{5}[/tex]), we get [tex]\frac{x}{5}[/tex]
Therefore,
[tex]\frac{2}{5}[/tex] x +[tex]\frac{x}{5}[/tex]+28=x
[tex]\frac{3}{5}[/tex] x +28 =x.
Subtracting [tex]\frac{3}{5}[/tex] on both sides, we get
[tex]\frac{3}{5}[/tex] x + 28-[tex]\frac{3}{5}[/tex] x =x-[tex]\frac{3}{5}[/tex] x
28 = [tex]\frac{5x}{5}[/tex] - [tex]\frac{3x}{5}[/tex]
28 = [tex]\frac{2x}{5}[/tex].
Multiplying both sides by 5, we get
28×5 = 5×[tex]\frac{2x}{5}[/tex].
140 =2x.
Dividing both sides, by 2, we get
[tex]\frac{140}{2}=\frac{2x}{2}[/tex]
x=70.
