Question

in the auditorium there are 15 red chairs and 36 blue chairs. what is the ratio of the number of blue chairs to the total number of chairs? :51

Explanation:

Step1: Find total number of chairs

Total chairs = Red chairs + Blue chairs = \( 15 + 36 = 51 \)

Step2: Find ratio of blue to total chairs

Ratio = Blue chairs : Total chairs = \( 36 : 51 \)
Simplify by dividing both by 3: \( \frac{36\div3}{51\div3}=\frac{12}{17} \), so ratio is \( 12:17 \)? Wait, no, wait. Wait the problem shows a box with :51, so we need to find the first number. Wait blue chairs are 36, total is 51. So 36:51, simplify. GCD of 36 and 51 is 3. 36÷3=12, 51÷3=17? Wait no, 36 and 51: 36=3×12, 51=3×17? Wait no, 51÷3=17? 3×17=51, yes. 36÷3=12. Wait but the problem's box is like [ ]:51. So the first number is 36 simplified? Wait no, wait the question is ratio of blue to total. Blue is 36, total is 51. So 36:51. Simplify numerator and denominator by 3: 36÷3=12, 51÷3=17? Wait no, 36 and 51: GCD(36,51)=3. So 36/51 = 12/17? Wait but the total is 51, so the ratio is 36:51, which simplifies to 12:17? Wait no, wait 36 and 51: 36 divided by 3 is 12, 51 divided by 3 is 17. But the problem's box is [ ]:51, so we need to put the blue chairs part. Wait maybe I made a mistake. Wait blue chairs are 36, total is 15+36=51. So ratio of blue to total is 36:51. If we want to write it as x:51, then x is 36? Wait no, 36:51 is the ratio. Wait maybe the problem is asking for the ratio in the form of [blue chairs simplified] : 51. Wait 36 and 51, divide numerator and denominator by 3: 36÷3=12, 51÷3=17. But 51 is the total, so maybe the problem has a typo? Wait no, looking at the image, the box is like a blank :51. So we need to find the first number. Blue chairs are 36, total is 51. So 36:51. So the first number is 36? But 36 and 51 can be simplified. Wait 36 and 51: GCD is 3. So 36÷3=12, 51÷3=17. But 51 is the total, so maybe the problem wants the ratio as 36:51, so the first number is 36? Wait no, let's recheck.

Wait the question: "What is the ratio of the number of blue chairs to the total number of chairs?" Blue chairs: 36, total chairs: 15+36=51. So ratio is 36:51. Simplify by dividing both by 3: 12:17. But the box is [ ]:51, so maybe the problem expects 36:51, so the first number is 36? Wait no, 36:51 is equal to 12:17, but 51 is 17×3, 36 is 12×3. So if we keep the total as 51, the blue part is 36. So the ratio is 36:51. So the blank is 36? Wait but 36 and 51 can be simplified. Wait maybe the problem is not simplifying, just putting the number of blue chairs to total. So blue is 36, total is 51, so ratio is 36:51. So the first number is 36.

Step1: Calculate total chairs

Total chairs = 15 (red) + 36 (blue) = \( 15 + 36 = 51 \)

Step2: Determine ratio of blue to total

Ratio of blue chairs to total chairs = Number of blue chairs : Total number of chairs = \( 36 : 51 \)

Answer:

36