Question

d. 15

1. carolyn buys flour for 16 cents per ounce and sugar for 24 cents per ounce. how many ounces of flour are in a mixture of flour and sugar that costs 22 cents per ounce and weighs 20 ounces?

a. 4 ounces
b. 5 ounces
c. 6 ounces
d. 7 ounces

1. giselle made several apple and peach pies. she bought peaches for $4 per pound and apples for $2 per pound. if giselle spent $60 to buy 24 pounds of fruit, how many pounds of peaches did she buy?

a. 6
b. 10
c. 18
d. 20

1. four years ago mary was twice as old as john. in three years john will be two - thirds as old as mary. how old is mary now?

a. 18
b. 19
c. 12
d. none of these

1. mary is twice as old as susan now, but 8 years ago she was 4 times as old as susan. how old was susan 4 years ago?

a. 20 years old
b. 12 years old
c. 8 years old
d. 4 years old

Explanation:

Problem 60:

Step1: Define variables

Let \( x \) be ounces of flour, \( y \) be ounces of sugar. We know \( x + y = 20 \) (total ounces) and \( 16x + 24y = 22\times20 \) (total cost).

Step2: Simplify cost equation

\( 16x + 24y = 440 \). Divide by 8: \( 2x + 3y = 55 \).

Step3: Solve system of equations

From \( x + y = 20 \), we get \( x = 20 - y \). Substitute into \( 2x + 3y = 55 \):
\( 2(20 - y) + 3y = 55 \)
\( 40 - 2y + 3y = 55 \)
\( y = 15 \). Then \( x = 20 - 15 = 5 \).

Step1: Define variables

Let \( p \) be pounds of peaches, \( a \) be pounds of apples. We have \( p + a = 24 \) (total pounds) and \( 4p + 2a = 60 \) (total cost).

Step2: Simplify cost equation

Divide \( 4p + 2a = 60 \) by 2: \( 2p + a = 30 \).

Step3: Solve system of equations

From \( p + a = 24 \), \( a = 24 - p \). Substitute into \( 2p + a = 30 \):
\( 2p + 24 - p = 30 \)
\( p = 6 \).

Step1: Define variables

Let Mary’s current age be \( M \), John’s current age be \( J \). Four years ago: \( M - 4 = 2(J - 4) \). In three years: \( J + 3 = \frac{2}{3}(M + 3) \).

Step2: Simplify first equation

\( M - 4 = 2J - 8 \) → \( M = 2J - 4 \).

Step3: Substitute into second equation

\( J + 3 = \frac{2}{3}(2J - 4 + 3) \)
\( J + 3 = \frac{2}{3}(2J - 1) \)
Multiply by 3: \( 3J + 9 = 4J - 2 \)
\( J = 11 \). Then \( M = 2(11) - 4 = 18 \).

Answer:

B. 5 ounces

Problem 61: