Find the cost per pound of turkey and the cost per pound of ham.

Question

Casey bought a 15.4-pound turkey and an 11.6-pound ham for Thanksgiving and paid $38.51.Her friend Jane bought a 10.2-pound turkey and a 7.3-pound ham from the same store and paid $24.84.

Answer 1

Set up a system of equations. T = cost per pound Turkey and H = cost per pound ham

15.4T + 11.6H = 38.51

10.2T + 7.3H = 24.84

Let’s try and get the T’s to cancel out. To do elimination with these less nice numbers, we will cross cross the T numbers from one equation to the other

1. multiply everything in the BOTTOM equation by 15.4
2. multiply everything in the TOP equation by 10.2

This will make the T’s match

157.08T + 118.32H = 392.802

157.08T + 112.42H = 382.536

The T’s exactly match each other. Let’s make them equal but opposite before we eliminate. I am going to take the whole bottom equation and flip all the signs so my 157.08T becomes -157.08T (doesn’t matter which equation you choose)

157.08T + 118.32H = 392.802

-157.08T - 112.42H = -382.536

now that they are equal and opposite = eliminate!

Everything left over on the left side adds together and everything left over on the right side adds together

118.32H - 112.42H = 392.802 - 382.536

combine like terms on both sides

5.9H = 10.266 divide by 5.9 both sides

H = $1.74 per pound of Ham

plug this back into either equation to find T

157.08T + 118.32H = 392.802

157.08T + (118.32)(1.74) = 392.802

157.08T + 205.8768 = 392.802

subtract 205.8768 from both sides

157.08T = 186.9252

divide by 157.08 on both sides

T = $1.19 per pound Turkey

Answer 2

15.4t + 11.6h = 38.51

10.2t + 7.3h = 24.84

Can you solve for either t or h and answer?