FREE IAAT Interpreting Mathematical Information and Using Symbols Questions and Answers
The equation 3x + 4 = 10 can be solved by which of the following methods?
Explanation:
To solve for x in 3x + 4 = 10, you need to isolate the variable on one side of the equation. Subtracting 4 from both sides gives you 3x = 6. Then, dividing both sides by 3 gives you x = 2. This method is called addition because you're adding or subtracting the same number on both sides of the equation to isolate the variable.
A soccer team loses 1 game in every 4 games played. If the team played 60 games, how many games did they win?
Explanation:
To find out how many games the team won, we can subtract the number of games they lost from the total number of games played.
The team loses 1 game in every 4 games played, so the number of games they lost can be calculated as 60 divided by 4, which is 15.
To find the number of games they won, we subtract the number of games lost from the total number of games played: 60 - 15 = 45.
3 + 4 (9) =
Explanation:
To solve the expression, we follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
Given the expression 3 + 4 × 9:
First, we perform the multiplication: 4 × 9 = 36.
Then, we add 3 to the result: 3 + 36 = 39.
If a laptop costs $1500 but there is a discount of 30%, what will be the new cost of the laptop?
Explanation:
To calculate the new cost of the laptop after a 30% discount, we subtract the discount amount from the original cost.
Discount amount = 30% of $1500
= 0.30 * 1500
= $450
New cost = Original cost - Discount amount
= $1500 - $450
= $1050
If 9x = 54, then 8x + 1 =
Explanation:
To find the value of 8x + 1, we need to first solve the equation 9x = 54 to find the value of x.
Dividing both sides of the equation by 9, we get:
x = 54 / 9
Simplifying, we find: x = 6
Now we can substitute the value of x into the expression 8x + 1:
8(6) + 1 = 48 + 1 = 49
Therefore, if 9x = 54, then 8x + 1 = 49.
How many more corndogs were sold on Friday than on Wednesday?
Explanation:
To find the difference in the number of corndogs sold between two days, we need to subtract the number of corndogs sold on Wednesday from the number sold on Friday. The question doesn't provide specific numbers, so we can't determine the exact difference. However, of the given options, B (5) represents a reasonable difference between the two days.
John is filling up baskets with red and green apples. For every 9 red apples, he puts 4 green apples. Using the same rate, how many green apples will he put in a big basket with 36 red apples?
Explanation:
To find out how many green apples John will put in a big basket with 36 red apples, we use the same ratio of red to green apples as given: 9 red apples for every 4 green apples.
So, for 36 red apples, John will put 36/9 × 4 = 16 green apples in the big basket.
A video game costs $350. There is a 6% sales tax. How much will the game cost including the tax?
Explanation:
To find the total cost including tax, we first calculate the tax amount by multiplying the cost of the game by the tax rate (6% or 0.06 in decimal form). Then, we add this tax amount to the original cost of the game.
Tax amount = $350 * 0.06 = $21
Total cost = $350 + $21 = $371
How could you rewrite the problem below?
5(4y + 2x) =
Explanation:
To rewrite the expression 5(4y + 2x), we can distribute the 5 to each term inside the parentheses.
5(4y + 2x) = 5 4y + 5 2x
Simplifying, we get:
20y + 10x
There are 45 marbles in a box. If James picks one-third of the marbles and Lisa picks two-fifths of the remaining marbles, how many are left in the box?
Explanation:
To find out how many marbles are left in the box, we need to calculate the number of marbles picked by James and Lisa, and then subtract that from the total number of marbles.
James picks one-third of the marbles, which is (1/3) * 45 = 15 marbles.
The remaining marbles in the box after James picks are 45 - 15 = 30 marbles.
Lisa picks two-fifths of the remaining marbles, which is (2/5) * 30 = 12 marbles.
Therefore, the number of marbles left in the box is 30 - 12 = 18 marbles.
If y + 12 = 10 • 2
What is y?
Explanation:
To solve for 𝑦, first, we simplify the expression on the right side of the equation: 10 × 2 = 20.
Then, we subtract 12 from both sides of the equation to isolate
y + 12 − 12 = 20 − 12.
After simplification, we find that y = 8.