To solve this problem, we should use a system of equations. In this example, we can construct two equations from the given equation letting the variable r represent the number of raspberries Diane has and b represent the number of blackberries Diane has.
r + b = 46 (the number of raspberries plus the number of blackberries is 46, the total number of berries)
b + 20 = r (there are 20 more raspberries than blackberries)
Our two equations are above. Because our second equation is already r in terms of b, we can substitute this value for r into our first equation, as modeled below:
r + b = 46
(b + 20) + b = 46
Now, to simplify, we should combine like terms on the left side of the equation.
2b + 20 = 46
Next, we should subtract 20 from both sides of the equation to get the variable term alone on the left side of the equation.
2b = 26
Finally, we should divide both sides of the equation by 2, in order to get rid of the coefficient on the variable b.
b = 13
Therefore, Diane has 13 blackberries (if you substitute in this value into the first equation, you can figure out that there are 33 raspberries in the bowl).
Hope this helps!
