Sam makes a cube out of blue, red and yellow bricks in the ratio 3:4:8. He uses between 400 to 410 cubes. Calculate the exact number of cubes he has used. Explain your answer.
I'm not really sure what to do to solve this.
the question seems incomplete
there is no perfect cube between 400 and 410
I think you are using "cube" in a non-mathematical way, I will assume you simply meant a rectangular block. If not, I agree with Scott.
Bricks used in the ratio of 3:4:8 or 3x:4x:8x for a total of 15x
15x = appr 400-410
x = appr 26.7 and 27.3
then x = 27
He used 3(27) blues, 4(27) reds and 8(27) yellows
or 81 blues, 108 reds and 216 yellows ----> 405 bricks total
a good solution that fits ... the "cube" isn't one
To solve this problem, we can start by representing the ratio of blue, red, and yellow bricks as 3x, 4x, and 8x respectively, where x is a common multiplier.
Next, we need to find the exact value of x. Since the total ratio is 3:4:8, the sum of the parts is 3 + 4 + 8 = 15x.
Given that Sam used between 400 to 410 cubes, we can set up an inequality based on the minimum and maximum number of cubes used:
400 ≤ 15x ≤ 410
To solve for x, divide all parts of the inequality by 15:
400 ÷ 15 ≤ x ≤ 410 ÷ 15
26.67 ≤ x ≤ 27.33
Since the number of cubes must be a whole number, we can round the values of x to the nearest whole number:
27 ≤ x ≤ 27
Therefore, the exact value of x is 27.
Now that we know the value of x, we can find the exact number of cubes Sam used:
Blue bricks = 3x = 3 * 27 = 81 cubes
Red bricks = 4x = 4 * 27 = 108 cubes
Yellow bricks = 8x = 8 * 27 = 216 cubes
The total number of cubes used is the sum of the blue, red, and yellow bricks:
81 + 108 + 216 = 405 cubes
So, the exact number of cubes Sam used is 405.