At the gym, Jasper was able to bench press 224 pounds, which was [tex]$\frac{7}{8}$[/tex] of the weight that Balin was able to bench press. Which shows the correct equation and value of [tex]$x$[/tex], the weight that Balin could bench press?
A. [tex]$\frac{7}{8} x=224 ; x=196$[/tex] pounds
B. [tex]$\frac{7}{8} x=224 ; x=256$[/tex] pounds
C. [tex]$\frac{7}{8}=\frac{x}{224} ; x=196$[/tex] pounds
D. [tex]$\frac{7}{8}=\frac{x}{224} ; x=256$[/tex] pounds
Answer (2)
Set up the equation: 8 7 x = 224 , where x represents Balin's bench press weight.
Multiply both sides by 7 8 to isolate x : x = 224 × 7 8 .
Simplify the expression: x = 32 × 8 .
Calculate the final value: x = 256 . Therefore, Balin's bench press weight is 256 pounds.
Explanation
Problem Analysis Let's analyze the problem. We know that Jasper's bench press weight is 224 pounds, and this is 8 7 of Balin's bench press weight. We need to find the correct equation and the value of x , which represents Balin's bench press weight.
Setting up the Equation We can set up the equation as follows: 8 7 x = 224 , where x is Balin's bench press weight. This equation states that 8 7 of Balin's weight is equal to Jasper's weight (224 pounds).
Isolating x To solve for x , we need to isolate x by multiplying both sides of the equation by the reciprocal of 8 7 , which is 7 8 . So, we have: x = 224 × 7 8
Calculating x Now, let's calculate the value of x :
x = 7 224 × 8 We can simplify this by dividing 224 by 7: x = 32 × 8
Finding the Value of x Finally, we multiply 32 by 8 to find the value of x :
x = 256 So, Balin's bench press weight is 256 pounds.
Final Answer The correct equation is 8 7 x = 224 , and the value of x is 256 pounds. Therefore, the correct answer is: 8 7 x = 224 ; x = 256 pounds
Examples
Understanding fractions and proportions is crucial in everyday life. For instance, if you're baking a cake and need to adjust the ingredient quantities based on a recipe that serves a different number of people, you'll use proportions. If a recipe calls for 3 2 cup of flour for 6 servings, and you want to make 9 servings, you can set up a proportion to find the new amount of flour needed. This same concept applies to scaling recipes, calculating discounts, or understanding financial ratios.
The equation to find Balin's bench press weight is 8 7 x = 224 , leading to the solution x = 256 pounds. Thus, the correct answer is option B. The calculations demonstrate that if Jasper can lift 224 pounds, Balin can lift a greater amount based on the proportional relationship given.
;
