Question

Kathy is making party trays. yesterday she made 1 small tray and 4 large trays with 166 total pieces of fruit. today she made 4 small trays and 4 large trays with 232 pieces of fruit. how many pieces of fruit are on each size tray?

Answer 1

We can start solving the problem by using a system of equations. Let x be the number of pieces of fruit on a small tray, and y be the number of pieces of fruit on a large tray.

From the information given, we know that:

Yesterday: x + 4y = 166 (1)

Today: 4x + 4y = 232 (2)

We have two equations and two unknowns, so we can use substitution to solve for one variable in terms of the other, and then substitute that back into the other equation.

From equation (1) we can solve for x:

x = 166 - 4y

Now we can substitute this into equation (2)

4(166 - 4y) + 4y = 232

Simplifying and solving for y:

-672 + 16y = 232

16y = 904

y = 56.5

This means that each large tray has 56.5 pieces of fruit.

Now we can substitute this value back into the first equation:

x + 4(56.5) = 166

x = 166 - 226

x = -60

This solution doesn't make sense, because the number of pieces of fruit can't be negative. This means that there is no solution to the system of equations, and it is impossible to determine the number of pieces of fruit on each size tray based on the information given.

Explanation: