Question

You and your brother go to the same store to buy groceries. You purchase a large watermelon for $7.71 and 2.4 lb of red grapes. Your brother buys a platter of pre-cut fruit for $ 9.95 and 1.6 lb of red grapes. You both spend the same amount of money, how much did the grapes cost per lb?

Answer 1

let's start by finding out how much money each person spent on grapes.

you spent $7.71 on a watermelon and some grapes, so we need to subtract the cost of the watermelon to find out how much you spent on grapes:

$7.71 - cost of watermelon = amount spent on grapes

we don't know the cost of the grapes yet, but we do know how much you spent in total. We can set up an equation:

$7.71 - cost of watermelon = $9.95

now we can solve for the cost of the watermelon:

$7.71 - $cost of watermelon = $9.95

$cost of watermelon = $7.71 - $9.95

$cost of watermelon = -$

but there is a problem.. we can't have a negative cost. This means there's an error in our setup.

let's try a different approach. we know that you and your brother spent the same amount of money, so we can set up an equation using that information:

$7.71 + cost of grapes = $9.95 + cost of grapes

now we can solve for the cost of grapes:

$7.71 - $9.95 = -$2.24

this still doesn't make sense, but we can see that the cost of grapes cancels out on both sides of the equation. This means that the cost of the grapes must be the same for both of you.

we know that you bought 2.4 lb of grapes and your brother bought 1.6 lb of grapes. If we let x be the cost per pound of grapes, we can set up an equation:

2.4x = 1.6x + $2.24

simplifying:

0.8x = $2.24

x = $2.80

So the cost per pound of grapes is $2.80.

Answer 2

Let's denote the cost of grapes per pound as x.

For you, the cost of the watermelon is $7.71 and the cost of 2.4 pounds of grapes is 2.4 * x.

So, your total cost is $7.71 + 2.4 * x.

For your brother, the cost of the fruit platter is $9.95 and the cost of 1.6 pounds of grapes is 1.6 * x.

So, your brother's total cost is $9.95 + 1.6 * x.

Since you both spend the same amount of money, we can set up the equation:

$7.71 + 2.4 * x = $9.95 + 1.6 * x.

Simplifying the equation, we get:

2.4 * x - 1.6 * x = $9.95 - $7.71.

0.8 * x = $2.24.

Dividing both sides by 0.8, we find:

x = $2.24 / 0.8.

x = $2.80.

Therefore, the grapes cost $2.80 per pound.