roated beef has 20g of protein and 11g of calcium per serving. serving of mashed potatoes has 2g of protein and 25g of calcium, how many servings of each are needed to supply 29 grams of protein and 61 grams of calcium?
Let the number of servings of beef be B, and let the number of servings of mash be M. Then we know that:
20B + 2M = 29
11B + 25M = 61
Multiply the first equation by 25, and the second one by 2 to get:
500B + 50M = 725
22B + 50M = 122
Subtract the second equation from the first one to get:
478B = 603
So B = 603/478 = 1.261, and M = (61-11B)/25 = 1.885
Check it:
(20 x 1.261) + (2 x 1.885) = 29
(11 x 1.261) + (25 x 1.885) = 61
So you need 1.261 portions of beef and 1.885 portions of mash.
To find out how many servings of each food are needed to supply a specific amount of protein and calcium, we can set up a system of equations.
Let's assume the number of servings of roast beef is x, and the number of servings of mashed potatoes is y.
From the given information, we know that one serving of roast beef has 20g of protein and 11g of calcium, and one serving of mashed potatoes has 2g of protein and 25g of calcium.
Based on the protein requirements, the equation becomes:
20x + 2y = 29 ---(Equation 1)
And based on the calcium requirements, the equation becomes:
11x + 25y = 61 ---(Equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
We will use the method of substitution:
Rearrange Equation 1 to solve for x:
20x = 29 - 2y
x = (29 - 2y) / 20
Substitute the value of x in Equation 2:
11((29 - 2y) / 20) + 25y = 61
Now, you can solve this equation to find the value of y, which represents the number of servings of mashed potatoes.
Simplify the equation:
(11 * 29 - 11 * 2y) / 20 + 25y = 61
(319 - 22y) / 20 + 25y = 61
Multiply both sides of the equation by 20 to eliminate the denominator:
319 - 22y + 500y = 1220
-22y + 500y = 1220 - 319
478y = 901
y = 901 / 478
y ≈ 1.885 (rounded to 3 decimal places)
Therefore, the number of servings of mashed potatoes needed to supply 29 grams of protein and 61 grams of calcium is approximately 1.885 servings.
Now, substitute this value of y back into Equation 1 to find the value of x:
x = (29 - 2(1.885)) / 20
x ≈ 1.061 (rounded to 3 decimal places)
Therefore, the number of servings of roast beef needed to supply 29 grams of protein and 61 grams of calcium is approximately 1.061 servings.
Note that it's not possible to have fractional servings, so you may need to adjust the servings accordingly to make them whole numbers.