… This will look a bit daunting for my son …
Hi Graham. Beginning students need exposure and practice, to understand symbolic math. I'm glad you're there to offer encouragement because symbolic reasoning skills are very important. If your son is currently studying pre-algebra topics, then this is a good opportunity to become familiar with using letters as symbols that represent numbers and using substitution methods to rewrite relationships (equations). We can remove "clutter" from some equations, by leaving out defining words and units.
Let R represent the rectangle's area
Let A represent the area of piece A
Let B represent the area of piece B
With these three symbol definitions, I expect your son understands why we can write:
R = A + B
We're told that:
B =
(3/8)R
We're also told that A is 28 more than B. As Jomo explained, that means we can write:
A = B + 28
Symbol A and the expression B+28 both represent the same number (they're equal). Therefore, we're now free to replace symbol A with the expression B+28 anywhere we choose. Let's make that replacement in our equation for the total area:
R = A + B
R = (B + 28) + B
It doesn't matter in what order we add numbers, so we can rewrite the new expression for R:
R = B + B + 28
We've discovered that the rectangle's area is twice the area of piece B plus 28 more. Here's where 6/8 comes from. We have another expression for the area of piece B (the exercise provided it, and it's written above in red). We substitute that expression for symbol B:
R = (3/8)R + (3/8)R + 28
R = (6/8)R + 28
I think you understand the rest:
R = (3/4)R + (1/4)R
R = (3/4)R + 28
Hence, 28 must be 1/4th of R.
28 × 4 = 112
It's good form to answer word problems with a sentence, including units. The rectangle's area is 112 cm
2.
The basic strategy was to start with the relationship R=A+B, followed by using given information to substitute expressions for symbols A and B, to obtain an equation that contains only the symbol whose value we're trying to find (R). If your son has specific questions, let us know. We could also help you create a model for this exercise, by cutting paper sheets into pairs of labeled pieces.
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