Question

Samantha's mother spent $78 at a farmers market. She bought the same number of pounds of apples for $1.50 per lb as tomatoes for $2.50 per lb. She also bought half that weight of a farmers cheese that sold for $4.00 per lb. The number of pounds of peaches she bought for $3.00 per lb was one more pound than the farmers cheese. How many pounds of each product did Samantha's mother buy?

Answer 1

The number of pounds of apples she bought = 10 pounds

The number of pounds of tomatoes she bought = 10 pounds

The number of pounds of the farmers cheese she bought = 5 pounds

The number of pounds of peaches she bought = 6 pounds

Explanation:

The given information are;

The amount that Samantha's mother spent in the market = $78

The number of pounds of apples she bought = The number of pounds of tomatoes she bought

The number of pounds of the farmers cheese she bought = 1/2 of the number of pounds of apples she bought

The number of pounds of peaches she bought = 1 + 1/2 of the number of pounds of apples she bought

The price of the apples = $1.50

The price of the tomatoes = $2.50

The price of the farmers cheese = $4.00

The price of the peaches = $3.00

If we put the number of pounds of the apples she bought = X, we have

X×$1.50 + X×$2.50 + 1/2×X×$4.00 + (1 + 1/2×X)×$3.00 = $78.00

Which gives;

X×$1.50 + X×$2.50 + 1/2×X×$4.00 + $3.00+ 1/2×X×$3.00 = $78.00

`(X * \$15.00 + \$ 6.00)/(2) = \$ 78`

X × $15.00 + $6.00 = $78 × 2 = $156.00

X × $15.00 + $6.00 = $156.00

X × $15.00 = $156.00 - $6.00 = $150.00

X = $150.00/($15.00) = 10 pounds

Therefore;

The number of pounds of the apples she bought = X = 10 pounds

The number of pounds of apples she bought = 10 pounds

The number of pounds of tomatoes she bought = The number of pounds of apples she bought = 10 pounds

The number of pounds of tomatoes she bought = 10 pounds

The number of pounds of the farmers cheese she bought = 1/2 of the number of pounds of apples she bought = 1/2 of 10 = 1/2×10 = 5 pounds

The number of pounds of the farmers cheese she bought = 5 pounds

The number of pounds of peaches she bought = 1 +The number of pounds of the farmers cheese she bought = 1 pound + 5 pounds = 6 pounds

The number of pounds of peaches she bought = 6 pounds.

Answer 2

The solution is: Samantha´s mother bought:

• 10.71 Lbs of apples

• 10.71 Lbs of tomatoes

• 5.36 Lbs of farmers cheese

• 6.36 Lbs of peaches

As the question of the problem is" How many pounds of each product Samantha´s mother bought" it is convenient to call:

• x quantity of pounds of apple ( the same as tomatoes )Samantha´s mother bought

• y quantity of pounds of farmers cheese Samantha´s mother bought

• z quantity of pounds of peaches Samantha´s mother bought

According to that:

Spent

She spent 78 $ buying

1.50× x + 2.50×x + 4× y + 3 × z = 78 (1)

Now y = x/2 and z = y + 1

By substitution in equation (1) we get

3.50× x + 4×(x/2) + 3× [( x/2 ) + 1 ] = 78

Solving for x

5.50×x + (3/2)×x + 3 = 78

11×x + 3×x + 6 = 156

14×x = 150

x = 10.71 Lbs

y = 10.71/2 y = 5.36 Lbs

and z = 5.36 + 1 = 6.36 Lbs

z = 6.36 Lbs