Question

Jordan paid $11.20 for 5 pears and 6 peaches.The cost of 3 prears is as much as 2 peaches. Find the cost of a pear and a peach.

Answer 1

Alright, before we start this question, we're going to give pears the variable (x) and we're going to give peaches the variable (y) to make writing the equations a bit easier.

Now that we have the variables set up, we can write out the equations! From the first part we know that 11.20= 5x+6y and from the second part we know that 3x=2y.

Now what we need to do is to pick an equation to solve for. Using the second equation is a bit cleaner, so that's what we're going to start with. To solve for x, we need to divide both sides by 3, so we will end up with x=2/3y.

Now that we know that, we can substitute the x in the first equation for 2/3y, which changes the first equation to 11.20= 5*(2/3y)+6y. Now we can solve for y!

To do this, we can distribute the 5 to get rid of the parenthesis to change the equation to 11.20= 10/3y+6y. 

Next, we have to add up the coefficients of y, so to do that, the fractions have to have the same denominator. Right now, the 6y has a denominator of 1, and we can change this by multiplying the top and bottom by 3 to match the other y variable. Now we should have 11.20= 10/3y+18/3y, which adds up to get 11.20=28/3y

Next, we can get rid of the fraction in front of the y by multiplying both sides by 3, giving us 33.6=28y.

To get the final cost of the y, all we have to do is divide both sides by 28, which gives us y=1.2

Now, we can plug the y value into either of the equations we had way back at the start, so to make it a bit easier, I'll use the second equation again, which is 3x=2y. When we plug in the y, it becomes 3x=2*1.2, which simplifies to 3x=2.4

Finally, we can solve for x by dividing both sides by 3, which leaves us with x= 0.8 to go with our answer of y=1.2

Now we can go back and check what we decided what the x and y stood for, and when we know that, we can say that the price of a pear is $0.80 and the price of a peach is $1.20 for our answer!