ctu3308

Ok didn't find this question in the sticky list so need some help here.

Blue book pg. 412 number 16

Let the operations "triangle symbol" and "square symbol" be defined for all real numbers a and b as follows.

a "triangle symbol" b = a +3b
a "square symbol" b = a +4b

If 4 "triangle symbol" (5y) = (5y) "square symbol" 4, what is the value of y?

This might sound dumb, but I have never seen these weird symbols used in equations before. What exactly do you do?

desperaclo

CB loves these types of problems. Just substitue the values into the equations given.

4[triangle]5y = 4 + 3(5y) = 4 + 15y

5y[square]4 = 5y + 4(4) = 5y + 16

4 + 15y = 5y + 16

10y=12

y=12/10 or 6/5 or 1.2.

obsessedAndre

These symbols are made up by the SAT. The only way to work the problem is to follow the definition of the symbols that they give you. Use the definitions to set up a normal equation without the symbols, and solve that.

They tell you
a "triangle symbol" b = a +3b
a "square symbol" b = a +4b

If 4 "triangle symbol" (5y) = (5y) "square symbol" 4, what is the value of y?

that translates to:
4 + 15y = 5y + 16
10y = 12
y = 1.2

ctu3308

so basically the triangle is "+3" and the square is "+4"?

desperaclo

Not exactly. The triangle and square denote operations that involve the terms on either side of each symbol.

So, if a[triangle]b = ab + a^2, then you can't say that [triangle] "is" anything.

optimizerdad

You may find it easier to use a more conventional function representation. For example, think of a [triangle] b as g(a,b) ; then
a [triangle] b = a + 3b can be written as g(a,b) = a+ 3b .
Similarly, if you think of a [square] b as h(a,b), then
a [square] b = a + 4b can be written as h(a,b) = a + 4b .

The question then becomes
"If g(4, 5y) = h(5y, 4), what is the value of y?"