Math  /  Algebra

Question70%70 \% of what number is 49 ? Use the equation to solve in your notes. Then check your answer on Zearr 70%w=4970% of  is 49.\begin{array}{c} 70 \% \cdot w=49 \\ 70 \% \text { of } \square \text { is } 49 . \end{array}

Studdy Solution

STEP 1

What is this asking? We need to find a number such that 70% of it is equal to 49. Watch out! Don't mix up 70% with 0.7.
Remember 70% is a convenient way to write the fraction 70/100, which is the same as 0.7 when written as a decimal!

STEP 2

1. Set up the equation
2. Solve for the unknown

STEP 3

Let's **define** ww as the mystery number we're looking for.
We know that 70% of ww is equal to 49.
We can write this as an equation:
0.70w=49 0.70 \cdot w = 49

STEP 4

Remember that 70% is the same as the fraction 70100\frac{70}{100}, which simplifies to 710\frac{7}{10} and can be written as the decimal **0.7**.

STEP 5

Our goal is to **isolate** ww on one side of the equation.
Right now, ww is being multiplied by **0.7**.
To undo this multiplication, we can divide both sides of the equation by **0.7**.
This is like having a balanced scale; if we do the same thing to both sides, the scale remains balanced.
0.7w0.7=490.7 \frac{0.7 \cdot w}{0.7} = \frac{49}{0.7}

STEP 6

On the left side, the **0.7** in the numerator and the **0.7** in the denominator divide to one, leaving us with just ww.
Awesome!
w=490.7 w = \frac{49}{0.7}

STEP 7

Now, let's tackle the right side.
Dividing 49 by 0.7 might seem tricky, but we can make it easier!
We can multiply both the numerator and the denominator by **10** to get rid of the decimal:
w=49100.710=4907 w = \frac{49 \cdot 10}{0.7 \cdot 10} = \frac{490}{7}

STEP 8

Now we have w=4907w = \frac{490}{7}.
We know that 77=497 \cdot 7 = 49, so 770=4907 \cdot 70 = 490.
Therefore, 4907=70\frac{490}{7} = 70.
w=70 w = 70

STEP 9

So, 70% of **70** is 49.
We found our mystery number!
It's **70**!

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