You baked 10 cupcakes for a party, and after
the party you only had 1/10 of the cupcakes
Write an expression applying the inverse
property of multiplication to find out how
many cupcakes remained after the party.
Select one:
a. 10 x 1/10 = 1
b. 10 + 1/10 = 1
C. 10 x 10 = 100
d. 1/10 x 1/10 = 1/100
Answers
Answer ⤵️
Information Stated:
Let’s say that Josh is J, Alice is A & Tom is T.
Josh made 10 more cakes than Alice, so the equation would be A + 10 = J
Alice made 8 more cakes than Tom, so the equation would be T + 8 = A
The total amount of cupcakes is 62, meaning that all 3 friends made 62 cupcakes altogether.
62 = J + A + T
Into the Maths:
Since J = A + 10, we can substitute A + 10 into J.
Now the equation would look like this: 62 = (A + 10) + A + T
*I have used brackets for clarity
We also know that T + 8 = A, meaning we can substitute T + 8 into A
This would make the equation look like this, 62 = (A + 10) + (T + 8) + T
Now, we can simplify this equation because it look a bit too messy.
62 = (A + 10) + (T + 8) + T
Since we are adding everything up together & simplifying things, we do not need the brackets. Simply remove the brackets.
62 = A + 10 + T + 8 + T
This equation only uses addition, so we can shift terms around like this:
62 = 10 + T + T + 8 +A, or like this
62 = T + 10 + A + T + 8
However, I believe that changing the equation like this:
62 = A + T + T + 10 + 8, is much easier to look at, especially for people who are starting to learn algebra.
In equations like this, we can add integers & like terms. Let’s put brackets around these integers & like terms, for clarity.
62 = A + (T + T) + (10 + 8)
This would equal to:
62 = A + 2T + 18
Note that 2T is like saying 2 * T. If I substituted T with 5, it would be (5 + 5), which is equal to 2 * 5.
Let’s take 18 from both sides, because we want to get rid of the +18 at the end.
62 -18 = A + 2T + 18 - 18
If you do something to one side, you have to do it to the other side, otherwise, the equation would not be equal. Take note that you cannot do this with expressions. Expressions do not have an equal sign. Examples would be, X + X, or 6 + T.
44 = A + 2T
Remember, we want to find out how many cupcakes Tom made. So we would like to have something along the lines of: T = ????
This means we need to get rid of A, not T.
Now, T + 8 = A (read the 3rd line), meaning the equation will be:
44 = T + 8 + 2T
44 = 8 + (T + 2T)
44 = 8 + 3T
Let’s remove 8 from both sides to get rid of that 8 on the right.
44 - 8 = 8 + 3T - 8
36 = 3T
Remember from before that 2T is the same as 2 * T? Well, it’s the same with 3T.
3T = 3 * T
So we can simplify this equation even more by dividing both sides by 3.
36 ÷ 3 = 3 * T ÷ 3
12 = T
Now, most of the time, you would put the term you want to solve at the star because you are stating that T is the one being solved, so the equation would be like this:
T = 12
Meaning, that Tom made a total of 12 cakes.