Answer :
Final answer:
Sonny correctly substituted 5 for x in the proportion 16/x = 48/12 and used cross multiplication to verify that the proportion is balanced, ending up with equal products, 192 = 192.
Explanation:
When Sonny substituted 5 for x in the proportion 16/x = 48/12, he performed a process called cross multiplication. In cross multiplication, you multiply the numerator of one fraction by the denominator of the other fraction, and set the products equal to each other. In this case, multiplying the numerator 16 by the denominator 12, and the denominator x (which is substituted by 5) by the numerator 48 results in two identical products: 192 and 240.
Cross multiplication:
- 16 * 12 = 192
- 48 * 5 = 240
Since 192 (which comes from 16 multiplied by 12) and 240 (which comes from 48 multiplied by 5) are equal, the equation 16/5 = 48/12 holds true, confirming that the substitution was done correctly and the proportion is balanced. This is an illustration of proportional reasoning where equivalent ratios show the relationship between pairs of numbers.
