Kristen has 64 coins in her bank. She has $9.25 in dimes and quarters. How many dimes and quarters does she have?
1 answer:
D= # of dimes q= # of quarters QUANTITY EQUATION: d + q= 64 COST EQUATION: 0.10d + 0.25q= $9.25 STEP 1: multiply quantity equation by -0.10 to be able to eliminate the d term in step 2 (-0.10)(d + q)= (-0.10)(64) -0.10d - 0.10q= -6.40 STEP 2: add equation from step 1 to cost equation to eliminate the d term and solve for q Add 0.10d + 0.25q= $9.25 -0.10d - 0.10q= -6.40 0.15q= 2.85 divide both sides by 0.15 q= 19 quarters STEP 3: substitute q value in step 2 into either original equation to find d value d + q= 64 d + 19= 64 subtract 19 from both sides d= 45 dimes CHECK: 0.10d + 0.25q= $9.25 0.10(45) + 0.25(19)= 9.25 4.50 + 4.75= 9.25 9.25= 9.25 ANSWER: There are 45 dimes and 19 quarters. Hope this helps! :)
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