Final answer:
To find the number of juice boxes in the crate, set up equations to solve for the quantities of apples and grapes. The ratio of apple to grape is 9:4, and there are 30 more apples than grapes. Solve for the variables using the equations and substitute the values back to find the final answer.
Step-by-step explanation:
To find the total number of juice boxes in the crate, we need to determine the quantity of both apples and grapes. Given that the ratio of apple to grape is 9:4, we know that the difference in quantity is 30 (more apples than grapes). We can set up a system of equations to solve for the variables:
Let x be the common multiplier for both quantities. Therefore, the number of apples is 9x and the number of grapes is 4x.
We know that the difference between the apples and grapes is 30, so we can write the equation 9x - 4x = 30. Simplifying this equation gives us 5x = 30, which means x = 6.
Finally, we can substitute the value of x back into one of the equations to find the number of juice boxes. Since there are 9 apples per juice box, we have 9 * 6 = 54 apples. Therefore, there are 54 juice boxes in the crate.