Question

The symbols $\triangle$, $\square$, $\diamond$, $\clubsuit$ represent four different integers from $1$ to $9$. Using the equations below, what is the value of $\square$

Answer 1

The value of the four integers are; Triangle = 1; Diamond = 5; Square = 2; Clubsuit = 7

How to solve simultaneous equations?

We are given the equations;

Triangle + Triangle + Triangle + Triangle + Triangle = Diamond

Triangle + Square + Square = Diamond

Square + Diamond = Clubsuit

If triangle is T, Diamond is D, Square is S and Clubsuit is C, then we have;

5T = D    ..... (eq 1)

T + 2S = D  .... (eq 2)

S + D = C   ......(eq 3)

Equations (1) and (2) are equal. Thus;

5T = T + 2S

4T = 2S

2T = S

T = S/2

Put T + 2S for D in equation (3):

S + T + 2S = C

3S + T = C

3S + S/2 = C

7S/2 = C

Since they are all integers from 1 to 9, it means that T cannot be more than 1 because 5T = D. Thus; T = 1

1 = S/2

S = 2

C = 7 * 2/2

C = 7

D = 5

Read more about Simultaneous equations at; brainly.com/question/148035

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