Answer:
Triangle = 2, Diamond = 5 and star = 5.
Step-by-step explanation:
Let Triangle = x, Diamond = y and Star = z.
Clue 1:
[tex]Star = Diamond[/tex]
[tex]z=y[/tex] .... (1)
Clue 2:
[tex](Star+Diamond)\times Triangle=20[/tex]
[tex](z+y)\times x=20[/tex]
Using (1) we get
[tex](y+y)\times x=20[/tex]
[tex]2xy=20[/tex]
[tex]xy=10[/tex] .... (2)
Clue 3:
[tex]Triangle\times Triangle\times Diamond=2\times Star\times Triangle[/tex]
[tex]x\times x\times y=2\times z\times x[/tex]
[tex]x^2y=2zx[/tex]
Using (1) we get
[tex]x^2y=2yx[/tex]
[tex]x^2y-2yx=0[/tex]
[tex]xy(x-2)=0[/tex]
Using zero product property,
[tex]xy=0[/tex]
[tex]x-2=0\Rightarrow x=2[/tex]
The value of xy can not be 0 because of equation (2). The value of x is 2.
Therefore, the value of triangle is 2.
Substitute x=2 in equation (2).
[tex]2y=10[/tex]
Divide both sides by 2.
[tex]y=\frac{10}{2}[/tex]
[tex]y=5[/tex]
The value of y is 5. Using (1) we get
[tex]z=5[/tex]
Therefore, Triangle = 2, Diamond = 5 and star = 5.
