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!
Answer:
I think it is 6 over 2 end fraction
Step-by-step explanation:
Answer:
x+5y-15
Step-by-step explanation:
(3x+5y-4)-(4x+11)
Remove the bracket
3x+5y-4-4x-11
Collect like terms
3x-4x+5y-4-11
-x+5y-15
Step-by-step explanation:
642 ÷ 36 = 17.8
so 17 boxes
17* 36 = 612 642-612 = 30
30 umbrellas were left
Answer:
a. answer choice c
b. 20301
Step-by-step explanation:
You first need to understand a formula for finding the sum of consecutive integers starting from one: (m*(m+1))/2, m is the biggest number in the set.
a. The biggest number in your set is 100, so we plug in 100 for m and solve:
100*101/2=50*101=5050
b. Same thing. Use the formula t plug in 201 for m:
201*202/2=201*101=20301
The only reason you have the picture next to your question is to prove the formula (m*(m+1))/2.