The cost of 5 party hats and 3 balloons is 35p. The cost of 3 party hats and 2 balloons is 22p. What is the cost of 8 party hats and 5 balloons? cost35p cost22p

## Step 1:First, we need to set up the system of equations. Let's denote the cost of a party hat as and the cost of a balloon as . From the problem, we can write the following equations:### ### ## Step 2:Next, we use the method of substitution or elimination to solve this system of equations. Here, we will use the method of elimination. To eliminate one of the variables, we can multiply the first equation by 2 and the second equation by 3, which gives us:### ### ## Step 3:Subtract the second equation from the first to eliminate :### ### ## Step 4:Substitute into the second equation to solve for :### ### \(3(4) + 2y = 22\)### ### ### ## Step 5:Now that we have the cost of a party hat ( ) and the cost of a balloon ( ), we can calculate the cost of 8 party hats and 5 balloons:### \(8x + 5y = 8(4) + 5(5) = 32 + 25 = 57\)